Loop Algorithms for Asymmetric Hamiltonians

TL;DR

This paper introduces generalized cluster-building rules for quantum Monte Carlo loop algorithms applied to the XXZ-model, leading to a new algorithm that outperforms standard methods in strong magnetic fields at low temperatures.

Contribution

It presents novel generalized rules for cluster construction in quantum Monte Carlo algorithms for the XXZ-model, improving performance in specific regimes.

Findings

New algorithm performs better than standard in strong magnetic fields

Applicable to the Heisenberg antiferromagnet

Enhances efficiency at low temperatures

Abstract

Generalized rules for building and flipping clusters in the quantum Monte Carlo loop algorithm are presented for the XXZ-model in a uniform magnetic field along the Z-axis. As is demonstrated for the Heisenberg antiferromagnet it is possible from these rules to select a new algorithm which performs significantly better than the standard loop algorithm in strong magnetic fields at low temperatures.