# The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code

## TL;DR

The ALF project provides a versatile, open-source quantum Monte Carlo code capable of simulating various lattice fermion models at finite temperature, supporting multiple models, lattices, and observables.

## Contribution

It offers a general, user-friendly implementation of the auxiliary field quantum Monte Carlo algorithm for diverse lattice fermion models, with predefined model types and MPI support.

## Key findings

- Supports simulation of Hubbard models on different lattices
- Includes examples like the honeycomb and square lattice Hubbard models
- Provides tools for implementing complex models like the Kondo lattice and SU(N) Hubbard-Heisenberg

## Abstract

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 $SU(N)$-Hubbard-Heisenberg model. One can download the code from our Git instance at https://alf.physik.uni-wuerzburg.de and sign in to file issues.