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

Martin Bercx, Florian Goth, Johannes S. Hofmann, Fakher F. Assaad

SciPost Phys. 3, 013 (2017) · published 16 August 2017 · licensed under CC BY-SA (4.0)


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 and sign in to file issues.

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Hubbard model Kondo lattice Quantum Monte Carlo simulations Quantum many-body systems

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