CPMC-Lab: A Matlab Package for Constrained Path Monte Carlo Calculations

TL;DR

CPMC-Lab is an open-source Matlab package that enables users to perform constrained-path Monte Carlo calculations on strongly correlated electron models, providing educational tools and a foundation for future development in quantum materials research.

Contribution

It introduces a comprehensive, user-friendly Matlab implementation of the constrained-path Monte Carlo method with visualization, facilitating learning and extension to real materials.

Findings

Demonstrated calculations of total, kinetic, and potential energies in 1D and 2D Hubbard models.

Showcased the package's ability to compute charge and spin gaps.

Validated the method's effectiveness in studying strongly correlated systems.

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.