High-order Time Expansion Path Integral Ground State

TL;DR

This paper introduces a high-order path integral Monte Carlo method that efficiently computes ground states with few beads, eliminating the need for trial wave functions and producing highly accurate, model-independent results.

Contribution

It presents a novel high-order short-time Green's function expansion that significantly enhances ground-state wave-function quality and efficiency in path integral Monte Carlo calculations.

Findings

Enables ground state calculations with very few beads

Removes the necessity of a trial wave function

Produces highly accurate, model-independent results

Abstract

The feasibility of path integral Monte Carlo ground state calculations with very few beads using a high-order short-time Green's function expansion is discussed. An explicit expression of the evolution operator which provides dramatic enhancements in the quality of ground-state wave-functions is examined. The efficiency of the method makes possible to remove the trial wave function and thus obtain completely model-independent results still with a very small number of beads. If a single iteration of the method is used to improve a given model wave function, the result is invariably a shadow-type wave function, whose precise content is provided by the high-order algorithm employed.