Quantum symmetry from enhanced sampling methods

TL;DR

This paper introduces an enhanced sampling method using Metadynamics to address the minus sign problem in quantum Monte Carlo simulations of two-electron systems, potentially applicable to more complex quantum systems.

Contribution

It presents a novel approach to mitigate the minus sign problem by reexpressing it as a free energy difference and applying Metadynamics for efficient sampling.

Findings

Successfully applied to two electrons in a quantum dot

Demonstrates potential extension to complex systems

Provides a new perspective on the minus sign problem

Abstract

We address the problem of the minus sign sampling for two electron systems using the path integral approach. We show that this problem can be reexpressed as one of computing free energy differences and sampling the tails of statistical distributions. Using Metadynamics, a realistic problem like that of two electrons confined in a quantum dot can be solved. We believe that this is a strategy that can possibly be extended to more complex systems.