LUE

Code to calculate various gluonic quantities in lattice QCD. These include quantities such as various Wilson loops or $F_{\mu\nu}$. See the first table below. Primarily this supports $SU(3)$, but there is a limited amount of $SU(2)$ support.

Note you may need to set the stacksize to larger (unlimited is easiest) to use this code

Method	Implementation Status	Notes
Generic 'path' based Wilson line	✓	Returns the multiplication along the path from a starting point
Plaquette (spatial, temporal, total)	✓
Polyakov Loop	✓	hard coded only
Clover Fmunu	✓ ✗	Function exists but is not currently used anywhere
5-loop improved Fmunu	✓	hep-lat/0203008
B^2 Calculation	✓	Currently using 5-loop Fmunu
Wmunu	✓ ✗	Deprecated functions to do nMuxnNu Wilson loops. Does not use generic path
Gluon Propagator	✗	Work in progress - POSTPONED.
uzerobar	✓	Calculates u_0 using Landau gauge and plaquette definitions
stout-link smearing	✓	Stout smear (Morningstar & Peardon, 10.1103/PhysRevD.69.054501) gauge links. Spatial link smearing only
$SU(3)$ & $SU(2)$ heatbath	✓	Heatbath algorithm to generate quenched $SU(3)$ or $SU(2)$. Naive implementation (no overrelaxation) but can use Wilson or tree-level Symanzik (Luescher-Weisz action). No improved action for $SU(2)$.

Note that $SU(2)$ supports only the Generic path based Wilson line and the generic path plaquette. $SU(2)$ modules and routines have SU2 in the name.

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Gauge Formats $(SU3)$

The supported formats are openqcd and an ILDG-like binary format. This is the ILDG binary data format in big endian. The cssm format stores some metadata, and then only the first two rows of the $SU(3)$ matrix. The cssm format assumes big endian.

Format	Read	Write
openqcd	✓	✓
ildg-bin	✓	✗
cssm	✓	✗

The internal representation of a $SU(3)$ gauge field is (3, 3, 4, NT, NS, NS, NS).

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Gauge Formats $(SU2)$

The cssm format stores some metadata, the real part of the whole $SU(2)$ matrix, the imaginary part of the whole $SU(2)$ matrix, then some more metadata. The cssm format assumes big endian.

The HKLS (Hands-Kim-Lawlor-Skullerud) supports the compact format used by su2hmc.

The NRQ2CD format is (ip5d2,2,2,4,0:1) where ip5d2 is $NX \times NY \times NZ \times NT / 2` where 0 means odd sites and 1 is even sites with NX iterating fastest.

Format	Read	Write
HKLS	✓	✓
cssm	✗	✓
NRQ2CD	✓	✓

The internal representation of a $SU(3)$ gauge field is (2, 2, 4, NT, NS, NS, NS).

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Run

Run a program using a command like the below. Here magnetic is the name of the app, we set the compiler to ifx, add the -qopenmp flag, specify the 'release' default flags of fpm, and us the mag.toml input file.

fpm run magnetic --compiler ifx --flag "-qopenmp" --profile release -- mag.toml

If using the intel compiler (ifx) you can enable openMP style parallelism with do-concurrent using the "-qopenmp" flag as well as ensuring that LOCALITYSUPPORT is defined in the fpm.toml file. gfortran<15 does not fully support the 2018 Fortran standard and so you need to remove the LOCALITYSUPPORT macro. Parallelisation may still work with gfortran using the flag -ftree-parallelize-loops=N but is less likely to perform well. Alternatively use the 'OMP' macro to activate openMP parallelism instead. The openMP parallelism is limited to genPlaquette measurements.

[preprocess]
[preprocess.cpp]
suffixes = ["F90"]
macros=['SETGITHASH=Yes', 'LOCALITYSUPPORT=1']

Program	purpose	args
magnetic	Calculates the magnetic portion of Fmunu	mag.toml
ILDG_to_OQCD	Convert a gauge field ILDG-bin in big endian to openqcd	inputFile outputFile NT NS
CSSM_to_OQCD	Convert a gauge field cssm to openqcd	inputFile outputFile NT NS
OQCD_to_ILDG	Convert a gauge field openqcd to ILDG-bin in big endian	inputFile outputFile NT NS
SU2_HKLS_to_CSSM	Convert a $SU(2)$ gaugefield in HKLS to cssm	inputFile outputFile NT NS
SU2_HKLS_to_NRQ2CD	Convert a $SU(2)$ gaugefield in HKLS to NRQ2CD	inputFile outputFile NT NS
OQCD_stoutSmear	Stout smear (spatial) an openqcd gauge field and print average unsmeared and smeared plaquette values	inputFile rho nSweeps NT NS
SU3_heatbath	Generate $SU(3)$ gaugefields and measure plaquette. Hard-coded parameters in this file
SU2_heatbath	Generate $SU(2)$ gaugefields and measure plaquette. Hard-coded parameters in this file

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Python Support

In the python folder we also supply a f2py and meson based system that will enable use of (some of) the functionality in python. This can be installed from the python folder using

pip install -e . --no-build-isolation

or via a conda environment file like:

name: snakeTesting
channels:
  - conda-forge
dependencies:
  - conda-forge::python=3.12.9
  - conda-forge::fpm            # Fortran package manager
  - conda-forge::meson-python   # For building fortran for use in python
  - conda-forge::ninja
  - conda-forge::pip
  - conda-forge::numpy
  - pip:
       - ../../libs/FLUE_Lat/python

where the repository has been cloned inside the ../../libs directory (this can also be done with git submodule).

Available routines are:

IO Routines:

write[ILDG/OQCD](filename, U, NS, NT) read[ILDG/OQCD/CSSM](filename, NS, NT)

plaquette routines:

plaq(U)/splaq(U)/tplaq(U) returns the average of all plaquettes, space-space plaquettes and space-time plaquettes respectively.

'gauge' routines:

stoutSmearLinks(U, rho, nweeps) returns a new copy of the gaugefield which has been stout-linked smeared (spatial links).

The IO routines return a numpy array of type double precision complex, of shape (NT, NS, NS, NS, 4, 3, 3). Note this is not the same as the Fortran, the translation is done in c_wrapper/FLUE_c.f90. This is so that it matches i.e. lyncs_io.

This f2py and meson build approach is inspired by fortran_meson_py by Salvador Brandolin with thanks to the Fortran-Lang Discourse

Tests

Some of the functionality has tests in the test folder using the testdata reference data. Run the tests using fpm test

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AI Assistance

The tests were predominatly generated using Microsoft Copilot (GPT 5.5). Refinements to the heatbath code also used Microsoft Copilot.