Monte Carlo Sampling for Wave Functions Requiring (Anti)Symmetrization

TL;DR

This paper introduces a Monte Carlo method to efficiently compute properties of complex, strongly correlated quantum states that require (anti)symmetrization, enabling studies of larger systems than previously possible.

Contribution

The authors develop a Monte Carlo framework that circumvents factorial scaling in (anti)symmetrization, facilitating analysis of larger strongly correlated quantum systems.

Findings

Enables computation of energies and correlators in large systems

Overcomes factorial scaling of explicit (anti)symmetrization

Allows study of states beyond exact diagonalization capabilities

Abstract

Many strongly correlated states, such as those arising in the fractional quantum Hall effect and spin liquids, are described by wave functions obtained by dividing particles into multiple clusters, constructing a readily evaluable wave function in each cluster, and (anti)symmetrizing across these clusters. We introduce a method to compute quantities such as energies and correlators, using Monte Carlo simulations for these states. Our framework overcomes the factorial scaling of explicit (anti)symmetrization, allowing for studies of systems beyond the reach of exact diagonalization.