High-order Path Integral Monte Carlo methods for solving quantum dot problems

TL;DR

This paper introduces optimized fourth-order Path Integral Monte Carlo methods that effectively solve quantum dot problems with up to 20 polarized electrons, overcoming the sign problem associated with conventional second-order methods.

Contribution

The paper presents a novel fourth-order PIMC approach that reduces the number of free-fermion propagators needed, improving accuracy and efficiency in quantum dot simulations.

Findings

Accurate quantum dot energies for up to 20 polarized electrons

Reduced sign problem compared to second-order methods

Effective use of Hamiltonian energy estimator

Abstract

The conventional second-order Path Integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of anti-symmetric free fermion propagators that are needed to extract the ground state wave function at large imaginary time. In this work, we show that optimized fourth-order Path Integral Monte Carlo methods, which use no more than 5 free-fermion propagators, can yield accurate quantum dot energies for up to 20 polarized electrons with the use of the Hamiltonian energy estimator.