Nested Cluster Algorithm for Frustrated Quantum Antiferromagnets

TL;DR

This paper introduces a nested cluster algorithm that effectively solves the sign problem in simulations of frustrated quantum antiferromagnets, enabling large-scale studies at moderate temperatures.

Contribution

It presents a novel nested cluster algorithm that overcomes the ergodicity and sign problems in quantum Monte Carlo simulations of frustrated antiferromagnets.

Findings

Eliminates the sign problem for large kagome and frustrated square lattices.

Applicable to various lattice geometries at moderate temperatures.

Improves simulation efficiency and accuracy in frustrated quantum systems.

Abstract

Simulations of frustrated quantum antiferromagnets suffer from a severe sign problem. We solve the ergodicity problem of the loop-cluster algorithm in a natural way and apply a powerful strategy to address the sign problem. For the spin 1/2 Heisenberg antiferromagnet on a kagome and on a frustrated square lattice, a nested cluster algorithm eliminates the sign problem for large systems. The method is applicable to general lattice geometries but limited to moderate temperatures.