CPMC-Lab: A Matlab package for Constrained Path Monte Carlo calculations

Abstract

We describe CPMC-Lab, a Matlab program for the constrained-path and phaseless auxiliary-field Monte Carlo methods. These methods have allowed applications ranging from the study of strongly correlated models, such as the Hubbard model, to ab initio calculations in molecules and solids. The present package implements the full ground-state constrained-path Monte Carlo (CPMC) method in Matlab with a graphical interface, using the Hubbard model as an example. The package can perform calculations in finite supercells in any dimensions, under periodic or twist boundary conditions. Importance sampling and all other algorithmic details of a total energy calculation are included and illustrated. This open-source tool allows users to experiment with various model and run parameters and visualize the results. It provides a direct and interactive environment to learn the method and study the code with minimal overhead for setup. Furthermore, the package can be easily generalized for auxiliary-field quantum Monte Carlo (AFQMC) calculations in many other models for correlated electron systems, and can serve as a template for developing a production code for AFQMC total energy calculations in real materials. Several illustrative studies are carried out in one- and two-dimensional lattices on total energy, kinetic energy, potential energy, and charge- and spin-gaps. Program summaryProgram title: CPMC-LabCatalogue identifier: AEUD_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUD_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2850No. of bytes in distributed program, including test data, etc.: 24838Distribution format: tar.gzProgramming language:Matlab.Computer: The non-interactive scripts can be executed on any computer capable of running Matlab with all Matlab versions. The GUI requires Matlab R2010b (version 7.11) and above. Operating system: Windows, Mac OS X, Linux.RAM: Variable.Classification: 7.3.External routines:MatlabNature of problem:Obtaining ground state energy of a repulsive Hubbard model in a supercell in any number of dimensions.Solution method:In the Constrained Path Monte Carlo (CPMC) method, the ground state of a many-fermion system is projected from an initial trial wave function by a branching random walk in an overcomplete basis of Slater determinants. Constraining the determinants according to a trial wave function |ΨT〉 removes the exponential decay of the signal-to-noise ratio characteristic of the sign problem. The method is exact if |ΨT〉 is exact.Unusual features:Direct and interactive environment with a Graphical User Interface for beginners to learn and study the Constrained Path Monte Carlo method with minimal overhead for setup.Running time:The sample provided takes a few seconds to run, the batch sample a few minutes.