Path integral Monte Carlo ground state approach: Formalism, implementation, and applications

TL;DR

This paper reviews the path integral Monte Carlo ground state (PIGS) method, detailing its theoretical foundation, implementation, and applications in solving the Schrödinger equation for quantum systems at zero temperature.

Contribution

It provides a comprehensive overview of the PIGS approach, including formalism, algorithmic details, and practical examples, highlighting its utility in quantum many-body problems.

Findings

Effective in determining eigenstates and expectation values

Applicable to both few- and many-body quantum systems

Demonstrated on sample sermonic systems

Abstract

Monte Carlo techniques have played an important role in understanding strongly-correlated systems across many areas of physics, covering a wide range of energy and length scales. Among the many Monte Carlo methods applicable to quantum mechanical systems, the path integral Monte Carlo approach with its variants has been employed widely. Since semi-classical or classical approaches will not be discussed in this review, path integral based approaches can for our purposes be divided into two categories: approaches applicable to quantum mechanical systems at zero temperature and approaches applicable to quantum mechanical systems at finite temperature. While these two approaches are related to each other, the underlying formulation and aspects of the algorithm differ. This paper reviews the path integral Monte Carlo ground state (PIGS) approach, which solves the time-independent Schroedinger equation. Specifically, the PIGS approach allows for the determination of expectation values with respect to eigen states of the few- or many-body Schroedinger equation provided the system Hamiltonian is known. The theoretical framework behind the PIGS algorithm, implementation details, and sample applications for sermonic systems are presented.