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arXiv:2012.11914 · SciPost Physics Codebases

The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code

Fakher F. Assaad, Martin Bercx, Florian Goth, Anika Götz, Johannes Stephan Hofmann, Emilie Huffman, Zihong Liu, Francesco Parisen Toldin, Jefferson S. E. Portela, Jonas Schwab

Published Nov 27, 2025• 22 citations
arXivHTMLPDF

Abstract

The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five pre-defined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as Z_2 Z 2 unconstrained lattice gauge theories coupled to fermionic and Z_2 Z 2 matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.4 and sign in to file issues.

DOI
10.21468/scipostphyscodeb.1-v2.4

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The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five pre-defined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as Z_2 Z 2 unconstrained lattice gauge theories coupled to fermionic and Z_2 Z 2 matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.4 and sign in to file issues.
The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five predefined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as Z_2 Z 2 unconstrained lattice gauge theories coupled to fermionic and Z_2 Z 2 matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.0 and sign in to file issues.
The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five pre-defined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as Z_2 Z 2 unconstrained lattice gauge theories coupled to fermionic and Z_2 Z 2 matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.4 and sign in to file issues.
The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five predefined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as Z_2 Z2 unconstrained lattice gauge theories coupled to fermionic and Z_2 Z2 matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.0 and sign in to file issues.
The Algorithms for Lattice Fermions package provides a general code for the finite temperature auxiliary field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to an Ising field with given dynamics. We provide predefined types that allow the user to specify the model, the Bravais lattice as well as equal time and time displaced observables. The code supports an MPI implementation. Examples such as the Hubbard model on the honeycomb lattice and the Hubbard model on the square lattice coupled to a transverse Ising field are provided and discussed in the documentation. We furthermore discuss how to use the package to implement the Kondo lattice model and the SU(N) S U ( N ) -Hubbard-Heisenberg model. One can download the code from our Git instance at and sign in to file issues.
We present release 3.0 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an open-source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. As in previous releases, development is centered on common data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs that let non-experts carry out serial or parallel numerical simulations using the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended-ensemble simulations, exact and full diagonalization (ED), the density matrix renormalization group (DMRG), and continuous-time QMC solvers for dynamical mean-field theory (DMFT). Major changes in release 3.0 include distribution of the pyalps binary through the Python Package Index (pip install pyalps) and through Spack for HPC systems; migration of development to GitHub with continuous integration and automated testing; relicensing of the package under the permissive MIT license; a rebuilt documentation and tutorial website, including a set of Jupyter-notebook tutorials and localized content; a broad modernization of the C++ codebase (C++17 compliance, Boost and NumPy 2.0 compatibility, and warning and dead-code cleanup) together with a major DMRG update and associated reliability and build-compatibility fixes; the removal of legacy components (the VisTrails provenance integration and the TEBD, MPS, and directed-worm-algorithm application codes); archival of release 3.0.0 with a Zenodo DOI; and a formal governance and sustainability model developed under the US National Science Foundation (NSF) POSE program. The software is available at https://alps.comp-phys.org.
We present a quantum Monte Carlo (QMC) technique for calculating the exact finite-temperature properties of Bose-Fermi mixtures. The Bose-Fermi auxiliary-field quantum Monte Carlo (BFAFQMC) algorithm combines two methods, a finite-temperature AFQMC algorithm for bosons and a variant of the standard AFQMC algorithm for fermions, into one algorithm for mixtures. We demonstrate the accuracy of our method by comparing its results for the Bose-Hubbard and Bose-Fermi-Hubbard models against those produced using exact diagonalization for small systems. Comparisons are also made with mean-field theory and the worm algorithm for larger systems. As is the case with most fermion Hamiltonians, a sign or phase problem is present in the BFAFQMC algorithm. We discuss the nature of these problems in this framework and describe how they can be controlled with well-studied approximations to expand the BFAFQMC algorithm's reach. This algorithm can serve as an essential tool for answering many unresolved questions about many-body physics in mixed Bose-Fermi systems.