EFT Pseudopotential: Quasiparticle Band Narrowing from Frozen Core Dynamics

Companion code for:

Kohn–Sham Hamiltonian from Effective Field Theory: Quasiparticle Band Narrowing from Frozen Core Dynamics Xiansheng Cai, Han Wang, Kun Chen arXiv:2604.25199

Overview

This repository contains the computational pipeline for computing the frozen-core quasiparticle renormalization factor $z^{\mathrm{core}}_{\nu\mathbf{k}}$ and the corrected quasiparticle band structure for Li, Na, K, Ca, Mg, Al, Si, and LiH.

The pipeline has two stages:

1. Stage 1 (run_ks.jl): Kohn–Sham DFT calculation (SCF + bands) using DFTK.jl
2. Stage 2 (freq_correction.jl): Post-SCF quasiparticle correction using the EFT form factors and excitation energies

Requirements

• Julia ≥ 1.10
• Packages: DFTK, Interpolations, SpecialFunctions, Unitful, UnitfulAtomic, JLD2, Plots, PseudoPotentialData, PyPlot
• Python with matplotlib installed (used by PyPlot for figure generation)

Install dependencies:

using Pkg
Pkg.activate(".")
Pkg.instantiate()  # resolves from Project.toml

If CUDA artifact download fails (no GPU needed), create LocalPreferences.toml:

[CUDA_Runtime_jll]
local = "true"
version = "none"

Usage

From the repository root:

# Run KS-DFT for sodium
julia --project=. sodium/run_ks.jl

# Compute QP correction for sodium
julia --project=. sodium/freq_correction.jl

# Generate all figures
bash generate_figures.sh

Directory Structure

├── Project.toml                    Julia project (run Pkg.instantiate())
├── generate_figures.sh             Reproduce all figures
├── lithium/                        Li (Z=3, 1s² core, analytic)
│   ├── run_ks.jl                   Stage 1: GTH LDA
│   ├── run_ks_eft.jl               Stage 1: EFT nonlocal PSP
│   ├── freq_correction_new.jl      Stage 2: coherent QP
│   ├── psp_eft_li.jl               EFT potential functions
│   └── psp_eft_nonlocal.jl         Nonlocal KB PSP
├── sodium/                         Na (Z=11, [Ne] core)
│   ├── atomic_hf.jl                Radial atomic DFT-LDA solver (shared)
│   ├── run_ks.jl                   Stage 1
│   └── freq_correction.jl          Stage 2
├── potassium/                      K (Z=19, [Ar] core)
├── calcium/                        Ca (Z=20, [Ar] core)
├── magnesium/                      Mg (Z=12, [Ne] core)
├── aluminum/                       Al (Z=13, [Ne] core)
├── silicon/                        Si (Z=14, [Ne] core)
├── lih/                            LiH (multi-site test)
└── plotting/                       Figure generation scripts

Key Formula

The quasiparticle energy is:

$$\epsilon^{\mathrm{QP}}_{\nu\mathbf{k}} = \epsilon_F + z^{\mathrm{core}}_{\nu\mathbf{k}} (\epsilon^{\mathrm{KS}}_{\nu\mathbf{k}} - \epsilon_F)$$

where the frozen-core factor is:

$$z^{\mathrm{core}}_{\nu\mathbf{k}} = \frac{1}{1 + \sum_c |F^c_{\nu\mathbf{k}}|^2 / \Delta E_c^2}$$

with $F^c_{\nu\mathbf{k}} = \sum_{\mathbf{G}} c_{\nu\mathbf{k}}(\mathbf{G}) f^c_{|\mathbf{k}+\mathbf{G}|}$ the coherent form factor.

License

MIT