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

### Submission summary

 As Contributors: Fakher Assaad · Martin Bercx · Johannes Stephan Hofmann Arxiv Link: https://arxiv.org/abs/1704.00131v2 Date accepted: 2017-07-17 Date submitted: 2017-06-26 Submitted by: Bercx, Martin Submitted to: SciPost Physics Discipline: Physics Subject area: Condensed Matter Physics - Theory Approaches: Theoretical, Computational

### 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.

### Ontology / Topics

See full Ontology or Topics database.

Published as SciPost Phys. 3, 013 (2017)

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.

### Submission & Refereeing History

Resubmission 1704.00131v2 on 26 June 2017
Submission 1704.00131v1 on 6 April 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

### Strengths

Great paper. See first report.

### Weaknesses

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.

### Report

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
(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).