From 1055e891a587785f1fcc8e876fbc8c46a5212a1f Mon Sep 17 00:00:00 2001 From: lkdvos Date: Mon, 6 Jul 2026 15:08:46 -0400 Subject: [PATCH 1/9] refactor transfer spectrum --- src/MPSKit.jl | 1 + src/algorithms/toolbox.jl | 96 --------------- src/algorithms/transfer_spectrum.jl | 179 ++++++++++++++++++++++++++++ 3 files changed, 180 insertions(+), 96 deletions(-) create mode 100644 src/algorithms/transfer_spectrum.jl diff --git a/src/MPSKit.jl b/src/MPSKit.jl index 694dd8024..b7387f3da 100644 --- a/src/MPSKit.jl +++ b/src/MPSKit.jl @@ -149,6 +149,7 @@ include("algorithms/derivatives/hamiltonian_derivatives.jl") include("algorithms/derivatives/projection_derivatives.jl") include("algorithms/expval.jl") include("algorithms/toolbox.jl") +include("algorithms/transfer_spectrum.jl") include("algorithms/grassmann.jl") include("algorithms/correlators.jl") diff --git a/src/algorithms/toolbox.jl b/src/algorithms/toolbox.jl index 4b9df6e58..934fdde42 100644 --- a/src/algorithms/toolbox.jl +++ b/src/algorithms/toolbox.jl @@ -66,39 +66,6 @@ function calc_galerkin(below, operator, above, envs) return maximum(pos -> calc_galerkin(pos, below, operator, above, envs), eachindex(below)) end -""" - transfer_spectrum(above::InfiniteMPS; below=above, tol=Defaults.tol, num_vals=20, - sector=leftunit(above)) - -Calculate the partial spectrum of the left mixed transfer matrix corresponding to the -overlap of a given `above` state and a `below` state. The `sector` keyword argument can be -used to specify a non-trivial total charge for the transfer matrix eigenvectors. -Specifically, an auxiliary space `ℂ[typeof(sector)](sector => 1)'` will be added to the -domain of each eigenvector. The `tol` and `num_vals` keyword arguments are passed to -`KrylovKit.eigsolve` -""" -function transfer_spectrum( - above::InfiniteMPS; below = above, tol = Defaults.tol, num_vals = 20, - sector = leftunit(above) - ) - init = randomize!( - similar( - above.AL[1], left_virtualspace(below, 1), - spacetype(above)(sector => 1)' * left_virtualspace(above, 1) - ) - ) - - transferspace = fuse(left_virtualspace(above, 1) * left_virtualspace(below, 1)') - num_vals = min(dim(transferspace, sector), num_vals) # we can ask at most this many values - eigenvals, eigenvecs, convhist = eigsolve( - flip(TransferMatrix(above.AL, below.AL)), init, num_vals, :LM; tol = tol - ) - convhist.converged < num_vals && - @warn "correlation length failed to converge: normres = $(convhist.normres)" - - return eigenvals -end - """ entanglement_spectrum(ψ, site::Int) -> SectorVector{T, sectortype(ψ), AbstractVector{T}} @@ -120,69 +87,6 @@ function entanglement_spectrum(st::FiniteMPS, site::Int) return LinearAlgebra.svdvals(st.C[site]) end -""" -Find the closest fractions of π, differing at most ```tol_angle``` -""" -function approx_angles(spectrum; tol_angle = 0.1) - angles = angle.(spectrum) ./ π # ∈ ]-1, 1] - angles_approx = rationalize.(angles, tol = tol_angle) # ∈ [-1, 1] - - # Remove the effects of the branchcut. - angles_approx[findall(angles_approx .== -1)] .= 1 # ∈ ]-1, 1] - - return angles_approx .* π # ∈ ]-π, π] -end - -""" -Given an InfiniteMPS, compute the gap ```ϵ``` for the asymptotics of the transfer matrix, as -well as the Marek gap ```δ``` as a scaling measure of the bond dimension. -""" -function marek_gap(above::InfiniteMPS; tol_angle = 0.1, kwargs...) - spectrum = transfer_spectrum(above; kwargs...) - return marek_gap(spectrum; tol_angle) -end - -function marek_gap(spectrum::AbstractVector{T}; tol_angle = 0.1) where {T <: Number} - # Remove 1s from the spectrum - inds = findall(abs.(spectrum) .< 1 - 1.0e-12) - length(spectrum) - length(inds) < 2 || @warn "Non-injective mps?" - - spectrum = spectrum[inds] - - angles = approx_angles(spectrum; tol_angle = tol_angle) - θ = first(angles) - - spectrum_at_angle = spectrum[findall(angles .== θ)] - - lambdas = -log.(abs.(spectrum_at_angle)) - - ϵ = first(lambdas) - - δ = Inf - if length(lambdas) > 2 - δ = lambdas[2] - lambdas[1] - end - - return ϵ, δ, θ -end - -""" - correlation_length(above::InfiniteMPS; kwargs...) - -Compute the correlation length of a given InfiniteMPS based on the next-to-leading -eigenvalue of the transfer matrix. The `kwargs` are passed to [`transfer_spectrum`](@ref), -and can for example be used to target the correlation length in a specific sector. -""" -function correlation_length(above::InfiniteMPS; kwargs...) - ϵ, = marek_gap(above; kwargs...) - return 1 / ϵ -end - -function correlation_length(spectrum::AbstractVector{T}; kwargs...) where {T <: Number} - ϵ, = marek_gap(spectrum; kwargs...) - return 1 / ϵ -end - """ variance(state, hamiltonian, [envs=environments(state, hamiltonian, state)]) diff --git a/src/algorithms/transfer_spectrum.jl b/src/algorithms/transfer_spectrum.jl new file mode 100644 index 000000000..67b1f5512 --- /dev/null +++ b/src/algorithms/transfer_spectrum.jl @@ -0,0 +1,179 @@ +""" + transfer_spectrum(above::InfiniteMPS, [below=above], [alg]; num_vals=20, kwargs...) + -> TensorKit.SectorVector + +Calculate the partial spectrum of the left transfer matrix corresponding to the overlap of a given `above` state and a `below` state. +The result is returned as a `TensorKit.SectorVector`, whose values can be inspected per sector by indexing, i.e. `transfer_spectrum(above)[sector]`. + +# Arguments + +- `above::InfiniteMPS`: the state for the "above" leg of the mixed transfer matrix. +- `below::InfiniteMPS=above`: the state for the "below" leg; defaults to the pure transfer matrix of `above`. +- `alg`: the eigensolver algorithm specification, resolved per sector via [`MatrixAlgebraKit.select_algorithm`](@extref MatrixAlgebraKit.select_algorithm). + This can be a KrylovKit algorithm instance (used verbatim for every sector), a `MatrixAlgebraKit.DefaultAlgorithm` or `NamedTuple` bundling keyword arguments, + or `nothing` (the default) to construct the eigensolver from the keyword arguments below. + +# Keyword arguments + +- `num_vals=20`: the number of eigenvalues to compute. This can either be a single `Int`, which is used for every sector of the transfer space, + or an `AbstractDict`/iterable of `sector => count` pairs to restrict the computation to specific sectors and request a different number of values per sector. +- `oversampling=10`: additive margin on the Krylov dimension beyond the number of values requested in a sector (see `krylovdim` below). +- `oversampling_factor=1`: proportionality factor between the Krylov dimension and the number of values requested in a sector (see `krylovdim` below). +- `krylovdim`: the Krylov dimension of the eigensolver. Unless given explicitly, this is chosen adaptively per sector as + `max(Defaults.krylovdim, ceil(Int, oversampling_factor * num_vals) + oversampling)`, where `num_vals` is the number of values requested in that sector. +- `kwargs...`: further keyword arguments (e.g. `tol`, `maxiter`) are forwarded to `MatrixAlgebraKit.default_algorithm` to build the eigensolver. + It is an error to pass eigensolver keyword arguments when `alg` is an algorithm instance. +""" +function transfer_spectrum( + above::InfiniteMPS, below::InfiniteMPS = above, alg = nothing; + num_vals = 20, kwargs... + ) + transferspace = fuse(left_virtualspace(above, 1) * left_virtualspace(below, 1)') + howmany = _transfer_howmany(num_vals, transferspace) + + T = complex(scalartype(above)) + S = spacetype(above) + Vsp = S(c => n for (c, n) in howmany) + spectrum = TensorKit.SectorVector{T}(undef, Vsp) + + A = flip(TransferMatrix(above.AL, below.AL)) + for (c, n) in howmany + algorithm = MatrixAlgebraKit.select_algorithm( + transfer_spectrum, above, alg; num_vals = n, kwargs... + ) + Va = S(c => 1) + Vt = left_virtualspace(above, 1) + Vb = left_virtualspace(below, 1) + init = randomize!(similar(above.AL[1], Vb ← Va' ⊗ Vt)) + eigenvals, _, convhist = eigsolve(A, init, n, :LM, algorithm) + convhist.converged < n && + @warn "transfer spectrum in sector $c not converged: normres = $(convhist.normres)" + spectrum[c] = view(eigenvals, 1:n) + end + return spectrum +end + +# convenience: positional `alg` without repeating `below` +transfer_spectrum(above::InfiniteMPS, alg; kwargs...) = + transfer_spectrum(above, above, alg; kwargs...) + +# normalize the `num_vals` specification into a `SectorDict` of per-sector counts, +# capped by the transfer-space dimension in each sector +_transfer_howmany(num_vals::Int, V) = + TensorKit.SectorDict(c => min(num_vals, dim(V, c)) for c in sectors(V)) +function _transfer_howmany(num_vals, V) + return TensorKit.SectorDict( + c => min(n, dim(V, c)) for (c, n) in pairs(num_vals) if dim(V, c) > 0 + ) +end + +# `num_vals` is intercepted here so it never reaches the algorithm constructor, and is +# exempt from the no-kwargs-with-`alg` rule (it is injected per sector by `transfer_spectrum`) +function MatrixAlgebraKit.select_algorithm( + ::typeof(transfer_spectrum), above::Union{InfiniteMPS, Type{<:InfiniteMPS}}, + alg = nothing; num_vals = 20, kwargs... + ) + if isnothing(alg) + return MatrixAlgebraKit.default_algorithm(transfer_spectrum, above; num_vals, kwargs...) + elseif alg isa NamedTuple || alg isa Base.Pairs + isempty(kwargs) || + throw(ArgumentError("keyword arguments are not allowed when `alg` is a NamedTuple")) + return MatrixAlgebraKit.default_algorithm(transfer_spectrum, above; alg..., num_vals) + elseif alg isa DefaultAlgorithm + isempty(kwargs) || + throw(ArgumentError("keyword arguments are not allowed when `alg` is given")) + return MatrixAlgebraKit.default_algorithm(transfer_spectrum, above; alg.kwargs..., num_vals) + elseif alg isa KrylovAlgorithm + isempty(kwargs) || + throw(ArgumentError("keyword arguments are not allowed when `alg` is given")) + return alg + end + throw(ArgumentError("Unknown alg $alg")) +end + +function MatrixAlgebraKit.default_algorithm( + ::typeof(transfer_spectrum), ::Type{<:InfiniteMPS}; num_vals = 20, + tol = Defaults.tol, maxiter = Defaults.maxiter, + oversampling = 10, oversampling_factor = 1, + krylovdim = max(Defaults.krylovdim, ceil(Int, oversampling_factor * num_vals) + oversampling), + verbosity = Defaults.VERBOSE_NONE, eager = true + ) + return Arnoldi(; tol, maxiter, krylovdim, verbosity, eager) +end + +""" +Find the closest fractions of π, differing at most ```tol_angle``` +""" +function approx_angles(spectrum; tol_angle = 0.1) + angles = angle.(spectrum) ./ π # ∈ ]-1, 1] + angles_approx = rationalize.(angles, tol = tol_angle) # ∈ [-1, 1] + + # Remove the effects of the branchcut. + angles_approx[findall(angles_approx .== -1)] .= 1 # ∈ ]-1, 1] + + return angles_approx .* π # ∈ ]-π, π] +end + +""" + marek_gap(above::InfiniteMPS; sector=nothing, kwargs...) + +Compute the gap ```ϵ``` for the asymptotics of the transfer matrix, as well as the Marek gap +```δ``` as a scaling measure of the bond dimension, along with the associated angle ```θ```. + +By default this returns a `TensorKit.SectorDict` mapping each sector of the transfer spectrum +to its `(ϵ, δ, θ)` triple. Passing a specific `sector` returns only that sector's triple. The +remaining `kwargs` are passed on to [`transfer_spectrum`](@ref). +""" +function marek_gap(above::InfiniteMPS; sector = nothing, tol_angle = 0.1, num_vals = 20, kwargs...) + if isnothing(sector) + spectrum = transfer_spectrum(above; num_vals, kwargs...) + return TensorKit.SectorDict(c => marek_gap(spectrum[c]; tol_angle) for c in keys(spectrum)) + end + spectrum = transfer_spectrum(above; num_vals = Dict(sector => num_vals), kwargs...) + return marek_gap(spectrum[sector]; tol_angle) +end + +function marek_gap(spectrum::AbstractVector{T}; tol_angle = 0.1) where {T <: Number} + # Remove 1s from the spectrum + inds = findall(abs.(spectrum) .< 1 - 1.0e-12) + length(spectrum) - length(inds) < 2 || @warn "Non-injective mps?" + + spectrum = spectrum[inds] + + angles = approx_angles(spectrum; tol_angle = tol_angle) + θ = first(angles) + + spectrum_at_angle = spectrum[findall(angles .== θ)] + + lambdas = -log.(abs.(spectrum_at_angle)) + + ϵ = first(lambdas) + + δ = Inf + if length(lambdas) > 2 + δ = lambdas[2] - lambdas[1] + end + + return ϵ, δ, θ +end + +""" + correlation_length(above::InfiniteMPS; sector=nothing, kwargs...) + +Compute the correlation length of a given InfiniteMPS based on the next-to-leading +eigenvalue of the transfer matrix. + +By default this returns a `TensorKit.SectorDict` mapping each sector of the transfer spectrum +to its correlation length. Passing a specific `sector` returns only that sector's correlation +length as a scalar. The remaining `kwargs` are passed on to [`transfer_spectrum`](@ref). +""" +function correlation_length(above::InfiniteMPS; sector = nothing, kwargs...) + gaps = marek_gap(above; sector, kwargs...) + isnothing(sector) || return 1 / first(gaps) # gaps :: (ϵ, δ, θ) + return TensorKit.SectorDict(c => 1 / first(g) for (c, g) in gaps) # gaps :: SectorDict +end + +function correlation_length(spectrum::AbstractVector{T}; kwargs...) where {T <: Number} + ϵ, = marek_gap(spectrum; kwargs...) + return 1 / ϵ +end From f4fd628a5fb0194a9caa276ef1defed4a0bb701e Mon Sep 17 00:00:00 2001 From: lkdvos Date: Mon, 6 Jul 2026 15:08:52 -0400 Subject: [PATCH 2/9] update plotting --- src/utility/plotting.jl | 22 ++++++++++++---------- 1 file changed, 12 insertions(+), 10 deletions(-) diff --git a/src/utility/plotting.jl b/src/utility/plotting.jl index d94f90c37..8380d54c4 100644 --- a/src/utility/plotting.jl +++ b/src/utility/plotting.jl @@ -89,7 +89,7 @@ function entanglementplot end end """ - transferplot(above, below=above; sectors=[], transferkwargs=(;)[, kwargs...]) + transferplot(above, below=above; sectors=nothing, transferkwargs=(;)[, kwargs...]) Plot the partial transfer matrix spectrum of two InfiniteMPS's. @@ -98,7 +98,8 @@ Plot the partial transfer matrix spectrum of two InfiniteMPS's. - `below::InfiniteMPS=above`: below mps for [`transfer_spectrum`](@ref). # Keyword Arguments -- `sectors=[]`: vector of sectors for which to compute the spectrum. +- `sectors=nothing`: restrict the spectrum to the given sectors; by default all sectors of + the transfer space are included. - `transferkwargs`: kwargs for call to [`transfer_spectrum`](@ref). - `kwargs`: other kwargs are passed on to the plotting backend. - `thetaorigin=0`: origin of the angle range. @@ -118,16 +119,17 @@ function transferplot end h::TransferPlot; sectors = nothing, transferkwargs = (;), thetaorigin = 0, sector_formatter = string ) - if sectors === nothing - sectors = [leftunit(h.args[1])] + below = length(h.args) == 1 ? h.args[1] : h.args[2] + kwargs = (; transferkwargs...) + if sectors !== nothing && get(kwargs, :num_vals, 20) isa Int + # restrict the computation to the requested sectors + num_vals = Dict(c => get(kwargs, :num_vals, 20) for c in sectors) + kwargs = (; kwargs..., num_vals) end + spectra = transfer_spectrum(h.args[1], below; kwargs...) - for sector in sectors - below = length(h.args) == 1 ? h.args[1] : h.args[2] - spectrum = transfer_spectrum( - h.args[1]; below = below, sector = sector, - transferkwargs... - ) + for (sector, spectrum) in pairs(spectra) + sectors === nothing || sector in sectors || continue @series begin yguide --> "r" From 9e3773be325b591b175fd0dc092429f9890f0ccb Mon Sep 17 00:00:00 2001 From: lkdvos Date: Mon, 6 Jul 2026 15:08:57 -0400 Subject: [PATCH 3/9] update tests --- test/algorithms/correlators.jl | 4 ++-- test/algorithms/statmech.jl | 2 +- test/misc/multifusion.jl | 5 +++-- 3 files changed, 6 insertions(+), 5 deletions(-) diff --git a/test/algorithms/correlators.jl b/test/algorithms/correlators.jl index 52fb914ea..2730a2ccf 100644 --- a/test/algorithms/correlators.jl +++ b/test/algorithms/correlators.jl @@ -14,12 +14,12 @@ using TensorKit: ℙ ψ = InfiniteMPS([ℙ^2], [ℙ^10]) H = force_planar(transverse_field_ising()) ψ, = find_groundstate(ψ, H, VUMPS(; verbosity = 0)) - len_crit = correlation_length(ψ)[1] + len_crit = correlation_length(ψ; sector = leftunit(ψ)) entrop_crit = entropy(ψ) H = force_planar(transverse_field_ising(; g = 4)) ψ, = find_groundstate(ψ, H, VUMPS(; verbosity = 0)) - len_gapped = correlation_length(ψ)[1] + len_gapped = correlation_length(ψ; sector = leftunit(ψ)) entrop_gapped = entropy(ψ) @test len_crit > len_gapped diff --git a/test/algorithms/statmech.jl b/test/algorithms/statmech.jl index 2101b0447..a87b5abf6 100644 --- a/test/algorithms/statmech.jl +++ b/test/algorithms/statmech.jl @@ -97,7 +97,7 @@ using TensorKit: ℙ num_vals = 2 vals_taylor = @constinferred(transfer_spectrum(convert(InfiniteMPS, rho_taylor); num_vals)) vals_mps = @constinferred(transfer_spectrum(rho_mps; num_vals)) - @test vals_taylor[1:num_vals] ≈ vals_mps[1:num_vals] + @test all(c -> vals_taylor[c] ≈ vals_mps[c], keys(vals_taylor)) end @testset "2D infinite partition functions with boundary MPS" verbose = true begin diff --git a/test/misc/multifusion.jl b/test/misc/multifusion.jl index 3315a112a..66639ea48 100644 --- a/test/misc/multifusion.jl +++ b/test/misc/multifusion.jl @@ -131,8 +131,9 @@ module TestMultifusion @test var < 1.0e-8 end - @test first(transfer_spectrum(ψ2; sector = C0)) ≈ 1 - @test !(abs(first(transfer_spectrum(ψ2; sector = C1))) ≈ 1) # testing injectivity + spec = transfer_spectrum(ψ2) + @test first(spec[C0]) ≈ 1 + @test !(abs(first(spec[C1])) ≈ 1) # testing injectivity @test only(keys(entanglement_spectrum(ψ2))) == M From 6bf37961b285340a885915d5774715aba58c64e7 Mon Sep 17 00:00:00 2001 From: lkdvos Date: Mon, 6 Jul 2026 15:09:07 -0400 Subject: [PATCH 4/9] update examples --- .../classic2d/1.hard-hexagon/figure-1.png | Bin 16573 -> 16739 bytes .../classic2d/1.hard-hexagon/index.md | 10 +- .../classic2d/1.hard-hexagon/main.ipynb | 6 +- .../quantum1d/5.haldane-spt/figure-1.png | Bin 32732 -> 32871 bytes .../quantum1d/5.haldane-spt/figure-2.png | Bin 32239 -> 32025 bytes .../examples/quantum1d/5.haldane-spt/index.md | 9 +- .../quantum1d/5.haldane-spt/main.ipynb | 2 +- .../quantum1d/8.bose-hubbard/figure-1.png | Bin 10885 -> 16373 bytes .../quantum1d/8.bose-hubbard/figure-2.png | Bin 13205 -> 17032 bytes .../quantum1d/8.bose-hubbard/figure-3.png | Bin 35352 -> 39405 bytes .../quantum1d/8.bose-hubbard/figure-4.png | Bin 35867 -> 36800 bytes .../quantum1d/8.bose-hubbard/figure-5.png | Bin 27423 -> 35226 bytes .../quantum1d/8.bose-hubbard/figure-6.png | Bin 15060 -> 15426 bytes .../quantum1d/8.bose-hubbard/index.md | 23 +-- .../quantum1d/8.bose-hubbard/main.ipynb | 180 +++++++++--------- examples/Cache.toml | 6 +- 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expectation_value(ψ_minus, H) ```` ```` --1.401483973963084 - 2.875923408269285e-17im +-1.4014839739630844 - 5.800167584873572e-17im ```` ````julia @@ -188,11 +188,12 @@ println("S_plus = $S_plus") ```` ```` -S_minus + log(2) = 1.5486227235421324 -S_plus = 1.5450323530571919 +S_minus + log(2) = 1.548622723541372 +S_plus = 1.5450323530299226 ```` --- *This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).* + diff --git a/docs/src/examples/quantum1d/5.haldane-spt/main.ipynb b/docs/src/examples/quantum1d/5.haldane-spt/main.ipynb index a5c803849..f85c243c3 100644 --- a/docs/src/examples/quantum1d/5.haldane-spt/main.ipynb +++ b/docs/src/examples/quantum1d/5.haldane-spt/main.ipynb @@ -213,4 +213,4 @@ }, "nbformat": 4, "nbformat_minor": 3 -} +} \ No newline at end of file diff --git a/docs/src/examples/quantum1d/8.bose-hubbard/figure-1.png b/docs/src/examples/quantum1d/8.bose-hubbard/figure-1.png index 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zA(nte+rOlvuKqVi>mnlTGIXkBv$3$~eX|6oRYP9>7ux1e%$xXQhFBd2v144wgaA8L@7m?`2>T@(_b2VF`h;ErGppC!ZZ%_&S{V$*zt{|}GPVkTCO=i-H TqZ*;~Bb4P; correlation_length(ψ; sector = leftunit(ψ)), states), ylabel = "Correlation length", xlabel = "Bond dimension", xscale = :log10, yscale = :log10, inset = bbox(0.2, 0.51, 0.25, 0.25), @@ -285,13 +285,13 @@ quasicondensate_density = map(state -> abs2(expectation_value(state, (0,) => a_o ```` 7-element Vector{Float64}: - 0.30974277207656425 - 0.28814775930068737 - 0.2702000951730164 - 0.25712728156142256 - 0.2468538617129866 - 0.2353979140629328 - 0.2279965552408022 + 0.31098779070601257 + 0.2881478589434881 + 0.2702000230423913 + 0.25712728516508654 + 0.24685385948652017 + 0.23539753899204166 + 0.22799654088348645 ```` We may now also visualize the momentum distribution function, which is obtained as the @@ -466,3 +466,4 @@ using what we have learnt in this tutorial. --- *This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).* + diff --git a/docs/src/examples/quantum1d/8.bose-hubbard/main.ipynb b/docs/src/examples/quantum1d/8.bose-hubbard/main.ipynb index d4ace3b04..615cea4a7 100644 --- a/docs/src/examples/quantum1d/8.bose-hubbard/main.ipynb +++ b/docs/src/examples/quantum1d/8.bose-hubbard/main.ipynb @@ -1,8 +1,10 @@ { "cells": [ { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "using Markdown\n", "using MPSKit, MPSKitModels, TensorKit\n", @@ -11,12 +13,11 @@ "\n", "theme(:wong)\n", "default(fontfamily = \"Computer Modern\", label = nothing, dpi = 100, framestyle = :box)" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "# 1D Bose-Hubbard model\n", "\n", @@ -96,21 +97,21 @@ "`ComplexSpace` (typeset as `\\bbC`). As $D$ is increased,\n", "one increases the amount of entanglement, i.e, quantum correlations that can be captured by\n", "the state." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "cutoff, D = 4, 5\n", "initial_state = InfiniteMPS(ℂ^(cutoff + 1), ℂ^D)" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "This simply initializes a tensor filled with random entries (check out the documentation for\n", "other useful constructors). Next, we need the creation and annihilation operators. While we\n", @@ -118,72 +119,73 @@ "[`MPSKitModels.jl`](https://github.com/QuantumKitHub/MPSKitModels.jl) instead that has\n", "predefined operators and models for most well-known lattice models. In particular, we can\n", "use `MPSKitModels.a_min` to create the bosonic annihilation operator." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "a_op = a_min(cutoff = cutoff) # creates a bosonic annihilation operator without any symmetries\n", "display(a_op[])\n", "display((a_op' * a_op)[])" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "The [] accessor lets us see the underlying array, and indeed the operators are exactly what\n", "we require. Similarly, the Bose Hubbard model is also predefined in\n", "`MPSKitModels.bose_hubbard_model` (although we will construct our own variant\n", "later on)." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "hamiltonian = bose_hubbard_model(InfiniteChain(1); cutoff = cutoff, U = 1, mu = 0.5, t = 0.2) # It is not strictly required to pass InfiniteChain() and is only included for clarity; one may instead pass FiniteChain(N) as well" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "This has created the Hamiltonian operator as a [matrix product operator](@ref\n", "InfiniteMPOHamiltonian) (MPO) which is a convenient form to use in conjunction with MPS.\n", "Finally, the ground state optimization may be performed with either `iDMRG` or\n", "`VUMPS`. Both should take similar arguments but it is known that VUMPS is typically\n", "more efficient for these systems so we proceed with that." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "ground_state, _, _ = find_groundstate(initial_state, hamiltonian, VUMPS(tol = 1.0e-6, verbosity = 2, maxiter = 200))\n", "println(\"Energy: \", expectation_value(ground_state, hamiltonian))" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "This automatically runs the algorithm until a certain [error measure](@ref\n", "MPSKit.calc_galerkin) falls below the specified tolerance or the maximum iterations is\n", "reached. Let us wrap all this into a convenient function." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "function get_ground_state(mu, t, cutoff, D; kwargs...)\n", " hamiltonian = bose_hubbard_model(InfiniteChain(); cutoff = cutoff, U = 1, mu = mu, t = t)\n", @@ -194,53 +196,52 @@ "end\n", "\n", "ground_state = get_ground_state(0.5, 0.01, cutoff, D; tol = 1.0e-6, verbosity = 2, maxiter = 500)" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "Now that we have the state, we may compute observables using the `expectation_value`\n", "function. It typically expects a `Pair`, `(i1, i2, .., ik) => op` where `op` is a\n", "`TensorMap` or `InfiniteMPO` acting over `k` sites. In case of the Hamiltonian, it is not\n", "necessary to specify the indices as it spans the whole lattice. We can now plot the\n", "correlation function $\\langle \\hat{a}^{\\dagger}_i \\hat{a}_j\\rangle$." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "plot(map(i -> real.(expectation_value(ground_state, (0, i) => a_op' ⊗ a_op)), 1:50), lw = 2, xlabel = \"Site index\", ylabel = \"Correlation function\", yscale = :log10)\n", "hline!([abs2(expectation_value(ground_state, (0,) => a_op))], ls = :dash, c = :black)" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "We see that the correlations drop off exponentially, indicating the existence of a gapped\n", "Mott insulating phase. Let us now shift our parameters to probe other phases." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "ground_state = get_ground_state(0.5, 0.2, cutoff, D; tol = 1.0e-6, verbosity = 2, maxiter = 500)\n", "\n", "plot(map(i -> real.(expectation_value(ground_state, (0, i) => a_op' ⊗ a_op)), 1:100), lw = 2, xlabel = \"Site index\", ylabel = \"Correlation function\", yscale = :log10, xscale = :log10)\n", "hline!([abs2(expectation_value(ground_state, (0,) => a_op))], ls = :dash, c = :black)" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "In this case, the correlation function drops off algebraically and eventually saturates as\n", "$\\lim_{i \\to \\infty}\\langle\\hat{a}_i^{\\dagger} \\hat{a}_j\\rangle ≈ \\langle \\hat{a}_i^{\\dagger}\\rangle \\langle \\hat{a}_j \\rangle = |\\langle a_i \\rangle|^2 \\neq 0$.\n", @@ -256,12 +257,13 @@ "effects. We can see this clearly by increasing the bond dimension. We also see that the\n", "correlation length seems to depend algebraically on the bond dimension as expected from\n", "finite-entanglement scaling arguments." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "cutoff = 4\n", "Ds = 20:5:50\n", @@ -293,7 +295,7 @@ ")\n", "\n", "scatter!(\n", - " p, Ds, correlation_length.(states),\n", + " p, Ds, map(ψ -> correlation_length(ψ; sector = leftunit(ψ)), states),\n", " ylabel = \"Correlation length\", xlabel = \"Bond dimension\",\n", " xscale = :log10, yscale = :log10,\n", " inset = bbox(0.2, 0.51, 0.25, 0.25),\n", @@ -305,32 +307,31 @@ " ylims = [20, 130],\n", " xlims = [15, 60]\n", ")" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "This shows that any finite bond dimension MPS necessarily breaks the symmetry of the system,\n", - "forming a Bose-Einstein condensate which introduces erraneous long-distance behaviour of\n", + "forming a Bose-Einstein condensate which introduces erroneous long-distance behaviour of\n", "correlation functions. In case of finite bond dimension, it is thus reasonable to associate\n", "the finite expectation value of the field operator to the 'quasicondensate' density of the\n", "system which vanishes as $D \\to \\infty$." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "quasicondensate_density = map(state -> abs2(expectation_value(state, (0,) => a_op)), states)" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "We may now also visualize the momentum distribution function, which is obtained as the\n", "Fourier transform of the single-particle density matrix. Starting from the definition of the\n", @@ -366,12 +367,13 @@ "that is not indicative of the true physics of the system. Since we know this contribution\n", "vanishes in the infinite bond dimension limit, we instead work with\n", "$\\langle \\hat{a}_r^{\\dagger} \\hat{a}_0 \\rangle_c = \\langle \\hat{a}_r^{\\dagger} \\hat{a}_0 \\rangle - |\\langle \\hat{a}\\rangle|^2$." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "ks = range(-0.05, 0.15, 500)\n", "momentum_distribution = map(\n", @@ -385,12 +387,11 @@ ")\n", "momentum_distribution = vcat(momentum_distribution...)'\n", "plot(ks, momentum_distribution, lab = \"D = \" .* string.(permutedims(Ds)), lw = 1.5, xlabel = \"Momentum k\", ylabel = L\"\\langle n_k \\rangle\", ylim = [0, 50])" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "We see that the density seems to peak around $k=0$, this time seemingly becoming more\n", "prominent as $D \\to \\infty$ which seems to suggest again that there is a condensate.\n", @@ -425,12 +426,13 @@ "of `MPSKitModels.jl` to see how these models are defined and tweak it as per your needs.\n", "Here we see that applying twisted boundary conditions is equivalent to adding a prefactor of\n", "$e^{\\pm i\\phi}$ in front of the hopping amplitudes." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "function bose_hubbard_model_twisted_bc(\n", " elt::Type{<:Number} = ComplexF64, symmetry::Type{<:Sector} = Trivial,\n", @@ -475,12 +477,11 @@ "superfluid_stiffness_profile(0.2, 0.3, 5, 4) # superfluid\n", "\n", "superfluid_stiffness_profile(0.01, 0.3, 5, 4) # mott insulator" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "Now that we know what phases to expect, we can plot the phase diagram by scanning over a\n", "range of parameters. In general, one could do better by performing a bisection algorithm for\n", @@ -490,12 +491,13 @@ "using the quasi-condensate density as an order parameter since extracting the superfluid\n", "density accurately requires a more robust scheme to compute second derivatives which takes\n", "us away from the focus of this tutorial." - ], - "metadata": {} + ] }, { - "outputs": [], "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "cutoff, D = 4, 10\n", "mus = range(0, 0.75, 40)\n", @@ -512,44 +514,42 @@ "end\n", "\n", "heatmap(ts, mus, order_parameters, xlabel = L\"t/U\", ylabel = L\"\\mu/U\", title = L\"\\langle \\hat{a}_i \\rangle\")" - ], - "metadata": {}, - "execution_count": null + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "Although the bond dimension here is quite low, we already see the deformation of the Mott\n", "insulator lobes to give way to the well known BKT transition that happens at commensurate\n", "density. One can go further and estimate the critical exponents using finite-entanglement\n", "scaling procedures on the correlation functions, but these may now be performed with ease\n", "using what we have learnt in this tutorial." - ], - "metadata": {} + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "---\n", "\n", "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*" - ], - "metadata": {} + ] } ], - "nbformat_minor": 3, "metadata": { + "kernelspec": { + "display_name": "Julia 1.12.6", + "language": "julia", + "name": "julia-1.12" + }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", - "version": "1.12.4" - }, - "kernelspec": { - "name": "julia-1.12", - "display_name": "Julia 1.12.4", - "language": "julia" + "version": "1.12.6" } }, - "nbformat": 4 + "nbformat": 4, + "nbformat_minor": 3 } \ No newline at end of file diff --git a/examples/Cache.toml b/examples/Cache.toml index 76b7cebb6..f2ca5b015 100644 --- a/examples/Cache.toml +++ b/examples/Cache.toml @@ -1,12 +1,12 @@ [classic2d] -"1.hard-hexagon" = "71d189b9138f98545c4239ed80a922cc4182e934db30af5ba867a0cee57305d0" +"1.hard-hexagon" = "68155a068c15152cc01aaf87e8265e310551041c58d8f0f4e9cd3bf0f89ee410" [quantum1d] "2.haldane" = "c5a0eb70f0930d38053535c659ab39a87121b6ebda040ceadd9deb5f30921315" "6.hubbard" = "cef140a6224350345735aac889ee7e33724fc0af9ce94f68be47a7e40107c09c" "7.xy-finiteT" = "0f330a157bea739a43a82a937791c680b2fa6e5e479171ee5ef318d1fdae7bcf" -"8.bose-hubbard" = "a060ac3e29a9169e9420f7125cdb020c83b26a380508ac85f108bff1562bc70c" +"8.bose-hubbard" = "cf0d9a543e784dc6053e413780d19e1b59bf956dd4598752fdf664804dd68ce6" "3.ising-dqpt" = "a2900eed23de7655f600943fae72d1dc35f87f33d11947f707d302ce245399fe" -"5.haldane-spt" = "28eb0350bd7e721866ccc1c14744e78ae5c650fda81e5f0eefb91de40ee4a76a" +"5.haldane-spt" = "c8fd3a8d406b9ff3ea9a34b596c5910d81e4eb710b665d7fa04e30f795a46086" "4.xxz-heisenberg" = "9033fb104c3f658ccb1b8e335b986b7abda59e0b5359be086d3b62e1cc32ebd6" "1.ising-cft" = "3d34757eee7b95120b746c5e30e713203a876a87353ecd9937798f29183c9916" diff --git a/examples/classic2d/1.hard-hexagon/main.jl b/examples/classic2d/1.hard-hexagon/main.jl index 3557caa24..49b3cc52f 100644 --- a/examples/classic2d/1.hard-hexagon/main.jl +++ b/examples/classic2d/1.hard-hexagon/main.jl @@ -49,7 +49,7 @@ V = virtual_space(D) ) # use non-hermitian eigensolver F = real(expectation_value(ψ, mpo)) S = real(first(entropy(ψ))) -ξ = correlation_length(ψ) +ξ = correlation_length(ψ; sector = leftunit(ψ)) println("F = $F\tS = $S\tξ = $ξ") md""" @@ -71,13 +71,13 @@ function scaling_simulations( ψ, envs, = leading_boundary(ψ₀, mpo, alg) entropies[1] = real(entropy(ψ)[1]) - correlations[1] = correlation_length(ψ) + correlations[1] = correlation_length(ψ; sector = leftunit(ψ)) for (i, d) in enumerate(diff(Ds)) ψ, envs = changebonds(ψ, mpo, OptimalExpand(; trscheme = truncrank(d)), envs) ψ, envs, = leading_boundary(ψ, mpo, alg, envs) entropies[i + 1] = real(entropy(ψ)[1]) - correlations[i + 1] = correlation_length(ψ) + correlations[i + 1] = correlation_length(ψ; sector = leftunit(ψ)) end return entropies, correlations end diff --git a/examples/quantum1d/8.bose-hubbard/main.jl b/examples/quantum1d/8.bose-hubbard/main.jl index 679649303..86edb774d 100644 --- a/examples/quantum1d/8.bose-hubbard/main.jl +++ b/examples/quantum1d/8.bose-hubbard/main.jl @@ -213,7 +213,7 @@ plot!( ) scatter!( - p, Ds, correlation_length.(states), + p, Ds, map(ψ -> correlation_length(ψ; sector = leftunit(ψ)), states), ylabel = "Correlation length", xlabel = "Bond dimension", xscale = :log10, yscale = :log10, inset = bbox(0.2, 0.51, 0.25, 0.25), From f45c763f0f4270ea7c853ff010d2215c9cb76ac8 Mon Sep 17 00:00:00 2001 From: lkdvos Date: Mon, 6 Jul 2026 15:10:14 -0400 Subject: [PATCH 5/9] update changelog --- docs/src/changelog.md | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/docs/src/changelog.md b/docs/src/changelog.md index 7e5dfbf04..25f3533bd 100644 --- a/docs/src/changelog.md +++ b/docs/src/changelog.md @@ -33,6 +33,15 @@ When releasing a new version, move the "Unreleased" changes to a new version sec shorthand: a two-argument call is always the overlap, since the second argument cannot be disambiguated between a ket and an operator (undecidable for density matrices, where states and operators share a representation). ([#436](https://github.com/QuantumKitHub/MPSKit.jl/pull/436)) +- `transfer_spectrum` now computes the spectrum for all sectors of the transfer space at once, + returning a `TensorKit.SectorVector` that can be indexed per sector. + The `sector` keyword is removed; a specific selection of sectors (with per-sector counts) can be + requested by passing `num_vals` as an `AbstractDict`/iterable of `sector => count` pairs. + The `below` state and the eigensolver algorithm are optional positional arguments, and the + algorithm can be resolved per sector. The Krylov dimension adapts to the number of values requested + in each sector, controlled by the new `oversampling` and `oversampling_factor` keywords. + Accordingly, `marek_gap` and `correlation_length` now return a `TensorKit.SectorDict` of + per-sector results by default; pass `sector = ...` to obtain a single sector's result as before. ### Deprecated From 9d61af0798e941308a2f73a717ff641378eab3fb Mon Sep 17 00:00:00 2001 From: lkdvos Date: Tue, 7 Jul 2026 09:55:07 -0400 Subject: [PATCH 6/9] avoid multifusion language --- .../classic2d/1.hard-hexagon/figure-1.png | Bin 16739 -> 16598 bytes .../classic2d/1.hard-hexagon/index.md | 23 +++++++++++------- .../classic2d/1.hard-hexagon/main.ipynb | 19 +++++++++------ examples/Cache.toml | 2 +- examples/classic2d/1.hard-hexagon/main.jl | 19 +++++++++------ 5 files changed, 39 insertions(+), 24 deletions(-) diff --git a/docs/src/examples/classic2d/1.hard-hexagon/figure-1.png b/docs/src/examples/classic2d/1.hard-hexagon/figure-1.png index 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zYejcIzJ2?4SZFA;pS^yKID+UWvzXL&sEuKJ+fDOM*4WBw!RI*M@87>2mqv!ig-`p} zLWTpzQM|>Jt1&-0iKMwi!RENqNw!19w&;i{Xrp9*LakG1*$?SZbQVN7V-pkT!@P5+ z5!%Qw^>8^$AS%EAHl!dUBLnpwygE;8F=k;QqPtBzOeI_B?d@$S3?CMvyvsw|n>sr?x1y)PO0Ft=j1;h+s^H7j$Y^S60=o=uF;gHSBBGD_zC&+m<1JuTsz z_C`j(02M_SUeXj(SMT-q_6ARh?_Ue1H)PGr5g}yR$AwW#g4~?1Vi7=3Y3aaoT>~HS zvAH=RaC2Zyqt^4WZ{Pl$p5}AkUUsvF($*PFYKVMB?bD}E1q1}*JT@Of^$`H0r-C~0 zKMg??(d`&_xK0D>%3n0t;AqfT-u%-`eYq20)IX1YpzsMQt6`$$PKBJ6+n1mn6dKIf zW91Jj={u)bEC$t;l|fgFd;i|CcO85=@CH0O(1U3us*q@|nWhrO@u_pp(Cc$z+wCLag>EYU0{4Cvy$5Atji%&|Mk`nP*JsAA%xx%qJdXLo^mf0K{rupc#b*&n{-#MiYg8EsgAS71%{$P?zSF zD_7)$=9iYhg;?(EQ*elbRGUSl4H&R>9kzx&r98*b=#b$qNNpq+yIsfv#(v(&G&2OCJ&*Z0&^Z_<{5x}d^(;W-PAV?$bI9?2SytwD|NdDiB{+P*i(9L!iOjN@YJgY>DY@cz zID1vp)M5qfrPEY!PoDG-2pIfc6cR2wnf4&{-W_QIdeL(8LwhBqw;>@R+1c6HSul45 zd_%e6)aWI3W>UDpq*5X~zrvho-OLMKNl!p$h^(yaiDNa;U>#iYGx zF*G)J{N@-geG2`Z(EAScj1UcVb#DDV`s_9OSD2#c`qjXU4)E<%XV2 Date: Wed, 8 Jul 2026 10:46:51 -0400 Subject: [PATCH 7/9] code suggestions --- src/algorithms/transfer_spectrum.jl | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/src/algorithms/transfer_spectrum.jl b/src/algorithms/transfer_spectrum.jl index 67b1f5512..65e982747 100644 --- a/src/algorithms/transfer_spectrum.jl +++ b/src/algorithms/transfer_spectrum.jl @@ -15,10 +15,10 @@ The result is returned as a `TensorKit.SectorVector`, whose values can be inspec # Keyword arguments -- `num_vals=20`: the number of eigenvalues to compute. This can either be a single `Int`, which is used for every sector of the transfer space, +- `num_vals = 20`: the number of eigenvalues to compute. This can either be a single `Int`, which is used for every sector of the transfer space, or an `AbstractDict`/iterable of `sector => count` pairs to restrict the computation to specific sectors and request a different number of values per sector. -- `oversampling=10`: additive margin on the Krylov dimension beyond the number of values requested in a sector (see `krylovdim` below). -- `oversampling_factor=1`: proportionality factor between the Krylov dimension and the number of values requested in a sector (see `krylovdim` below). +- `oversampling = 10`: additive margin on the Krylov dimension beyond the number of values requested in a sector (see `krylovdim` below). +- `oversampling_factor = 1`: proportionality factor between the Krylov dimension and the number of values requested in a sector (see `krylovdim` below). - `krylovdim`: the Krylov dimension of the eigensolver. Unless given explicitly, this is chosen adaptively per sector as `max(Defaults.krylovdim, ceil(Int, oversampling_factor * num_vals) + oversampling)`, where `num_vals` is the number of values requested in that sector. - `kwargs...`: further keyword arguments (e.g. `tol`, `maxiter`) are forwarded to `MatrixAlgebraKit.default_algorithm` to build the eigensolver. @@ -28,11 +28,11 @@ function transfer_spectrum( above::InfiniteMPS, below::InfiniteMPS = above, alg = nothing; num_vals = 20, kwargs... ) + S = TensorKit.check_spacetype(above, below) transferspace = fuse(left_virtualspace(above, 1) * left_virtualspace(below, 1)') howmany = _transfer_howmany(num_vals, transferspace) T = complex(scalartype(above)) - S = spacetype(above) Vsp = S(c => n for (c, n) in howmany) spectrum = TensorKit.SectorVector{T}(undef, Vsp) @@ -63,7 +63,7 @@ _transfer_howmany(num_vals::Int, V) = TensorKit.SectorDict(c => min(num_vals, dim(V, c)) for c in sectors(V)) function _transfer_howmany(num_vals, V) return TensorKit.SectorDict( - c => min(n, dim(V, c)) for (c, n) in pairs(num_vals) if dim(V, c) > 0 + c => min(n, dim(V, c)) for (c, n) in num_vals if dim(V, c) > 0 ) end From e23a5e353d52fbdaaeba769c8344b45017a7fc4f Mon Sep 17 00:00:00 2001 From: Lukas Devos Date: Thu, 9 Jul 2026 18:25:25 -0400 Subject: [PATCH 8/9] Apply suggestions from code review Co-authored-by: Lander Burgelman <39218680+leburgel@users.noreply.github.com> --- examples/classic2d/1.hard-hexagon/main.jl | 6 +++--- src/algorithms/transfer_spectrum.jl | 8 ++++---- 2 files changed, 7 insertions(+), 7 deletions(-) diff --git a/examples/classic2d/1.hard-hexagon/main.jl b/examples/classic2d/1.hard-hexagon/main.jl index cb3117bd0..3cf117fe6 100644 --- a/examples/classic2d/1.hard-hexagon/main.jl +++ b/examples/classic2d/1.hard-hexagon/main.jl @@ -21,7 +21,7 @@ The [hard hexagon model](https://en.wikipedia.org/wiki/Hard_hexagon_model) is a This can be encoded in a transfer matrix with a local MPO tensor using anyonic symmetries, and the resulting MPO has been implemented in MPSKitModels. In order to use these anyonic symmetries, we need to generalise the notion of the bond dimension and define how it interacts with the symmetry. -Thus, we implement away of converting integers to symmetric spaces of the given dimension, which provides a crude guess for how the final MPS would distribute its Schmidt spectrum. +Thus, we implement a way of converting integers to symmetric spaces of the given dimension, which provides a crude guess for how the final MPS would distribute its Schmidt spectrum. """ mpo = hard_hexagon() P = physicalspace(mpo, 1) @@ -60,7 +60,7 @@ The dominant eigenvector is of course only an approximation. The finite bond dimension enforces a finite correlation length, which effectively introduces a length scale in the system. This can be exploited to formulate a scaling hypothesis [pollmann2009](@cite), which in turn allows to extract the central charge. -First we need to know the entropy and correlation length at a bunch of different bond dimensions. +First we need to know the entropy and correlation length at several different bond dimensions. Our approach will be to re-use the previous approximated dominant eigenvector, and then expanding its bond dimension and re-running VUMPS. According to the scaling hypothesis we should have ``S ∝ \frac{c}{6} log(ξ)``. Therefore we should find ``c`` using """ @@ -72,7 +72,7 @@ function scaling_simulations( entropies = similar(Ds, Float64) correlations = similar(Ds, Float64) alg = VUMPS(; verbosity, tol, alg_eigsolve) - sector = unit(sectortype(mpo)) # dominant correlation functions are in the trivial sector + sector = unit(sectortype(mpo)) # in this example the dominant correlation functions are in the trivial sector ψ, envs, = leading_boundary(ψ₀, mpo, alg) entropies[1] = real(entropy(ψ)[1]) diff --git a/src/algorithms/transfer_spectrum.jl b/src/algorithms/transfer_spectrum.jl index 65e982747..50b0f6122 100644 --- a/src/algorithms/transfer_spectrum.jl +++ b/src/algorithms/transfer_spectrum.jl @@ -22,7 +22,7 @@ The result is returned as a `TensorKit.SectorVector`, whose values can be inspec - `krylovdim`: the Krylov dimension of the eigensolver. Unless given explicitly, this is chosen adaptively per sector as `max(Defaults.krylovdim, ceil(Int, oversampling_factor * num_vals) + oversampling)`, where `num_vals` is the number of values requested in that sector. - `kwargs...`: further keyword arguments (e.g. `tol`, `maxiter`) are forwarded to `MatrixAlgebraKit.default_algorithm` to build the eigensolver. - It is an error to pass eigensolver keyword arguments when `alg` is an algorithm instance. + Passing eigensolver keyword arguments when `alg` is an algorithm instance is not allowed, and will result in an error. """ function transfer_spectrum( above::InfiniteMPS, below::InfiniteMPS = above, alg = nothing; @@ -117,11 +117,11 @@ end """ marek_gap(above::InfiniteMPS; sector=nothing, kwargs...) -Compute the gap ```ϵ``` for the asymptotics of the transfer matrix, as well as the Marek gap -```δ``` as a scaling measure of the bond dimension, along with the associated angle ```θ```. +Compute the gap `ϵ` for the asymptotics of the transfer matrix, as well as the Marek gap +`δ` as a scaling measure of the bond dimension, along with the associated angle `θ`. By default this returns a `TensorKit.SectorDict` mapping each sector of the transfer spectrum -to its `(ϵ, δ, θ)` triple. Passing a specific `sector` returns only that sector's triple. The +to its `(ϵ, δ, θ)` triplet. Passing a specific `sector` returns only that sector's triplet. The remaining `kwargs` are passed on to [`transfer_spectrum`](@ref). """ function marek_gap(above::InfiniteMPS; sector = nothing, tol_angle = 0.1, num_vals = 20, kwargs...) From 7de9689c229d7d53e30c9460e73eb4c92ed8c134 Mon Sep 17 00:00:00 2001 From: lkdvos Date: Thu, 9 Jul 2026 18:29:45 -0400 Subject: [PATCH 9/9] rename `num_vals` -> `howmany` --- docs/src/changelog.md | 2 +- src/algorithms/transfer_spectrum.jl | 42 ++++++++++++++--------------- src/utility/plotting.jl | 6 ++--- test/algorithms/statmech.jl | 6 ++--- 4 files changed, 28 insertions(+), 28 deletions(-) diff --git a/docs/src/changelog.md b/docs/src/changelog.md index 25f3533bd..f7cd0741e 100644 --- a/docs/src/changelog.md +++ b/docs/src/changelog.md @@ -36,7 +36,7 @@ When releasing a new version, move the "Unreleased" changes to a new version sec - `transfer_spectrum` now computes the spectrum for all sectors of the transfer space at once, returning a `TensorKit.SectorVector` that can be indexed per sector. The `sector` keyword is removed; a specific selection of sectors (with per-sector counts) can be - requested by passing `num_vals` as an `AbstractDict`/iterable of `sector => count` pairs. + requested by passing `howmany` as an `AbstractDict`/iterable of `sector => count` pairs. The `below` state and the eigensolver algorithm are optional positional arguments, and the algorithm can be resolved per sector. The Krylov dimension adapts to the number of values requested in each sector, controlled by the new `oversampling` and `oversampling_factor` keywords. diff --git a/src/algorithms/transfer_spectrum.jl b/src/algorithms/transfer_spectrum.jl index 50b0f6122..4581ff01f 100644 --- a/src/algorithms/transfer_spectrum.jl +++ b/src/algorithms/transfer_spectrum.jl @@ -1,5 +1,5 @@ """ - transfer_spectrum(above::InfiniteMPS, [below=above], [alg]; num_vals=20, kwargs...) + transfer_spectrum(above::InfiniteMPS, [below = above], [alg]; howmany = 20, kwargs...) -> TensorKit.SectorVector Calculate the partial spectrum of the left transfer matrix corresponding to the overlap of a given `above` state and a `below` state. @@ -15,22 +15,22 @@ The result is returned as a `TensorKit.SectorVector`, whose values can be inspec # Keyword arguments -- `num_vals = 20`: the number of eigenvalues to compute. This can either be a single `Int`, which is used for every sector of the transfer space, +- `howmany = 20`: the number of eigenvalues to compute. This can either be a single `Int`, which is used for every sector of the transfer space, or an `AbstractDict`/iterable of `sector => count` pairs to restrict the computation to specific sectors and request a different number of values per sector. - `oversampling = 10`: additive margin on the Krylov dimension beyond the number of values requested in a sector (see `krylovdim` below). - `oversampling_factor = 1`: proportionality factor between the Krylov dimension and the number of values requested in a sector (see `krylovdim` below). - `krylovdim`: the Krylov dimension of the eigensolver. Unless given explicitly, this is chosen adaptively per sector as - `max(Defaults.krylovdim, ceil(Int, oversampling_factor * num_vals) + oversampling)`, where `num_vals` is the number of values requested in that sector. + `max(Defaults.krylovdim, ceil(Int, oversampling_factor * howmany) + oversampling)`, where `howmany` is the number of values requested in that sector. - `kwargs...`: further keyword arguments (e.g. `tol`, `maxiter`) are forwarded to `MatrixAlgebraKit.default_algorithm` to build the eigensolver. Passing eigensolver keyword arguments when `alg` is an algorithm instance is not allowed, and will result in an error. """ function transfer_spectrum( above::InfiniteMPS, below::InfiniteMPS = above, alg = nothing; - num_vals = 20, kwargs... + howmany = 20, kwargs... ) S = TensorKit.check_spacetype(above, below) transferspace = fuse(left_virtualspace(above, 1) * left_virtualspace(below, 1)') - howmany = _transfer_howmany(num_vals, transferspace) + howmany = _transfer_howmany(howmany, transferspace) T = complex(scalartype(above)) Vsp = S(c => n for (c, n) in howmany) @@ -39,7 +39,7 @@ function transfer_spectrum( A = flip(TransferMatrix(above.AL, below.AL)) for (c, n) in howmany algorithm = MatrixAlgebraKit.select_algorithm( - transfer_spectrum, above, alg; num_vals = n, kwargs... + transfer_spectrum, above, alg; howmany = n, kwargs... ) Va = S(c => 1) Vt = left_virtualspace(above, 1) @@ -57,32 +57,32 @@ end transfer_spectrum(above::InfiniteMPS, alg; kwargs...) = transfer_spectrum(above, above, alg; kwargs...) -# normalize the `num_vals` specification into a `SectorDict` of per-sector counts, +# normalize the `howmany` specification into a `SectorDict` of per-sector counts, # capped by the transfer-space dimension in each sector -_transfer_howmany(num_vals::Int, V) = - TensorKit.SectorDict(c => min(num_vals, dim(V, c)) for c in sectors(V)) -function _transfer_howmany(num_vals, V) +_transfer_howmany(howmany::Int, V) = + TensorKit.SectorDict(c => min(howmany, dim(V, c)) for c in sectors(V)) +function _transfer_howmany(howmany, V) return TensorKit.SectorDict( - c => min(n, dim(V, c)) for (c, n) in num_vals if dim(V, c) > 0 + c => min(n, dim(V, c)) for (c, n) in howmany if dim(V, c) > 0 ) end -# `num_vals` is intercepted here so it never reaches the algorithm constructor, and is +# `howmany` is intercepted here so it never reaches the algorithm constructor, and is # exempt from the no-kwargs-with-`alg` rule (it is injected per sector by `transfer_spectrum`) function MatrixAlgebraKit.select_algorithm( ::typeof(transfer_spectrum), above::Union{InfiniteMPS, Type{<:InfiniteMPS}}, - alg = nothing; num_vals = 20, kwargs... + alg = nothing; howmany = 20, kwargs... ) if isnothing(alg) - return MatrixAlgebraKit.default_algorithm(transfer_spectrum, above; num_vals, kwargs...) + return MatrixAlgebraKit.default_algorithm(transfer_spectrum, above; howmany, kwargs...) elseif alg isa NamedTuple || alg isa Base.Pairs isempty(kwargs) || throw(ArgumentError("keyword arguments are not allowed when `alg` is a NamedTuple")) - return MatrixAlgebraKit.default_algorithm(transfer_spectrum, above; alg..., num_vals) + return MatrixAlgebraKit.default_algorithm(transfer_spectrum, above; alg..., howmany) elseif alg isa DefaultAlgorithm isempty(kwargs) || throw(ArgumentError("keyword arguments are not allowed when `alg` is given")) - return MatrixAlgebraKit.default_algorithm(transfer_spectrum, above; alg.kwargs..., num_vals) + return MatrixAlgebraKit.default_algorithm(transfer_spectrum, above; alg.kwargs..., howmany) elseif alg isa KrylovAlgorithm isempty(kwargs) || throw(ArgumentError("keyword arguments are not allowed when `alg` is given")) @@ -92,10 +92,10 @@ function MatrixAlgebraKit.select_algorithm( end function MatrixAlgebraKit.default_algorithm( - ::typeof(transfer_spectrum), ::Type{<:InfiniteMPS}; num_vals = 20, + ::typeof(transfer_spectrum), ::Type{<:InfiniteMPS}; howmany = 20, tol = Defaults.tol, maxiter = Defaults.maxiter, oversampling = 10, oversampling_factor = 1, - krylovdim = max(Defaults.krylovdim, ceil(Int, oversampling_factor * num_vals) + oversampling), + krylovdim = max(Defaults.krylovdim, ceil(Int, oversampling_factor * howmany) + oversampling), verbosity = Defaults.VERBOSE_NONE, eager = true ) return Arnoldi(; tol, maxiter, krylovdim, verbosity, eager) @@ -124,12 +124,12 @@ By default this returns a `TensorKit.SectorDict` mapping each sector of the tran to its `(ϵ, δ, θ)` triplet. Passing a specific `sector` returns only that sector's triplet. The remaining `kwargs` are passed on to [`transfer_spectrum`](@ref). """ -function marek_gap(above::InfiniteMPS; sector = nothing, tol_angle = 0.1, num_vals = 20, kwargs...) +function marek_gap(above::InfiniteMPS; sector = nothing, tol_angle = 0.1, howmany = 20, kwargs...) if isnothing(sector) - spectrum = transfer_spectrum(above; num_vals, kwargs...) + spectrum = transfer_spectrum(above; howmany, kwargs...) return TensorKit.SectorDict(c => marek_gap(spectrum[c]; tol_angle) for c in keys(spectrum)) end - spectrum = transfer_spectrum(above; num_vals = Dict(sector => num_vals), kwargs...) + spectrum = transfer_spectrum(above; howmany = Dict(sector => howmany), kwargs...) return marek_gap(spectrum[sector]; tol_angle) end diff --git a/src/utility/plotting.jl b/src/utility/plotting.jl index 8380d54c4..022fee33b 100644 --- a/src/utility/plotting.jl +++ b/src/utility/plotting.jl @@ -121,10 +121,10 @@ function transferplot end ) below = length(h.args) == 1 ? h.args[1] : h.args[2] kwargs = (; transferkwargs...) - if sectors !== nothing && get(kwargs, :num_vals, 20) isa Int + if sectors !== nothing && get(kwargs, :howmany, 20) isa Int # restrict the computation to the requested sectors - num_vals = Dict(c => get(kwargs, :num_vals, 20) for c in sectors) - kwargs = (; kwargs..., num_vals) + howmany = Dict(c => get(kwargs, :howmany, 20) for c in sectors) + kwargs = (; kwargs..., howmany) end spectra = transfer_spectrum(h.args[1], below; kwargs...) diff --git a/test/algorithms/statmech.jl b/test/algorithms/statmech.jl index a87b5abf6..9a9e8f906 100644 --- a/test/algorithms/statmech.jl +++ b/test/algorithms/statmech.jl @@ -94,9 +94,9 @@ using TensorKit: ℙ E_tdvp = expectation_value(rho_mps_tdvp, H) @test E_tdvp ≈ E_taylor atol = 1.0e-2 - num_vals = 2 - vals_taylor = @constinferred(transfer_spectrum(convert(InfiniteMPS, rho_taylor); num_vals)) - vals_mps = @constinferred(transfer_spectrum(rho_mps; num_vals)) + howmany = 2 + vals_taylor = @constinferred(transfer_spectrum(convert(InfiniteMPS, rho_taylor); howmany)) + vals_mps = @constinferred(transfer_spectrum(rho_mps; howmany)) @test all(c -> vals_taylor[c] ≈ vals_mps[c], keys(vals_taylor)) end