Deterministic Loop Stochastic Series Expansion Algorithm for Quantum Spin Models in Magnetic Fields

TL;DR

This paper introduces a deterministic loop SSE algorithm tailored for antiferromagnetic quantum spin models in magnetic fields, improving efficiency over traditional directed loop methods.

Contribution

The authors develop a new deterministic loop SSE method for systems with broken symmetry, enabling more efficient simulations of magnetic phases under external fields.

Findings

Reduces CPU time per Monte Carlo step compared to directed loop approach

Enables separate analysis of longitudinal and transverse modes in ordered phases

Outperforms standard algorithms in efficiency for antiferromagnetic chains

Abstract

The stochastic series expansion (SSE) algorithm is one of the most powerful quantum Monte Carlo methods and has been extensively applied to the study of quantum many body systems. Its efficiency is particularly enhanced with a deterministic loop update scheme in the study of the S=1/2 quantum spin systems that preserve SU(2) spin rotational symmetry. Once the symmetry is broken, such as by an external field, a directed loop method is typically required, resulting in a significant reduction in efficiency. Inspired by the SSE approach developed for the quantum Ising model, we introduce a deterministic loop SSE method that is particularly suited for antiferromagnetic systems under a staggered magnetic field. This method enables separate investigations of longitudinal and transverse modes in magnetically ordered phases arising from spontaneous symmetry breaking. We benchmark the performance of our algorithm against the standard directed loop approach applied to the antiferromagnetic Heisenberg chain and demonstrate that our method substantially reduces CPU time per Monte Carlo step, thereby can outperform the directed loop algorithm in efficiency.