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

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

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Fakher Assaad · Martin Bercx · Florian Goth · Johannes Stephan Hofmann
Submission information
Preprint Link:  (pdf)
Date accepted: 2017-07-17
Date submitted: 2017-06-26 02:00
Submitted by: Bercx, Martin
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approaches: Theoretical, Computational


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.

Author comments upon resubmission

Dear Editor,
We would like to thank the referees for their pertinent comments, and their appreciation of providing such an open source package to the community. In the second version of the documentation of the ALF package, we have addressed the points raised by the referees, and detailed them in the replies to the referees (see version 1 of the manuscript). We hope that the manuscript is now in a form that can be published in SciPost.
With best regards,

M. Bercx, F. Goth, J.S. Hofmann, and F.F. Assaad.

List of changes

List of major changes:
1) Section 1.1: We have included a paragraph on similar open source program packages for correlated quantum matter.
2) Section 1.2: We have extended the discussion on the properties of the general Hamiltonian and we have included a description of the scope and the limitations of ALF.
3) Section 2.3: We have extended the discussion on numerical stabilization.
4) Section 2.4: We have largely extended the section on Monte Carlo sampling and autocorrelations, including a detailed example of error estimation.
5) We have added the computation of autocorrelation functions to the error analysis program of ALF.
6) Section 6: We have extended the discussion on future developments of ALF.

Published as SciPost Phys. 3, 013 (2017)

Reports on this Submission

Anonymous Report 1 on 2017-7-14 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1704.00131v2, delivered 2017-07-14, doi: 10.21468/SciPost.Report.190


Great paper. See first report.


Earlier minor weaknesses taken care of in the revised version.
Eq (23) uses the real part for the sign of a configuration, whereas on page 1 the modulus is specified; this could be clarified.


I am happy with the revised version of this excellent paper and strongly recommend publication.

Requested changes

See above.

  • validity: top
  • significance: top
  • originality: high
  • clarity: top
  • formatting: perfect
  • grammar: excellent

Author:  Martin Bercx  on 2017-07-17  [id 154]

(in reply to Report 1 on 2017-07-14)

We would like to thank the referee for their positive evaluation of the revised version.
In the following we respond to the point raised by the referee:
"Eq (23) uses the real part for the sign of a configuration, whereas on page 1 the modulus is specified; this could be clarified."

While the configuration weight $e^{-S(C)}$ will in general be a complex number we have the freedom to factor out its real part (Eq. 24).
This is motivated by the observation that the partition function can always be written as a sum of real numbers (see also footnote 4).
The implementation then has the advantage of returning average signs that are real (Eq. 25).

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