Blockspin Cluster Algorithms for Quantum Spin Systems

TL;DR

This paper introduces cluster algorithms for quantum spin systems, mapping them to classical models with multi-spin interactions, significantly improving simulation efficiency and overcoming slowing down issues in standard methods.

Contribution

The paper develops novel cluster algorithms for quantum spin systems by mapping them to classical models with multi-spin couplings, enhancing simulation performance.

Findings

Algorithms effectively reduce slowing down in simulations.

Significant efficiency improvements in one-dimensional spin chains.

Applicable to both ferro- and anti-ferromagnetic systems.

Abstract

Cluster algorithms are developed for simulating quantum spin systems like the one- and two-dimensional Heisenberg ferro- and anti-ferromagnets. The corresponding two- and three-dimensional classical spin models with four-spin couplings are maped to blockspin models with two-blockspin interactions. Clusters of blockspins are updated collectively. The efficiency of the method is investigated in detail for one-dimensional spin chains. Then in most cases the new algorithms solve the problems of slowing down from which standard algorithms are suffering.