Stochastic series expansion method with operator-loop update

TL;DR

This paper introduces an operator-loop cluster update for the stochastic series expansion quantum Monte Carlo method, improving efficiency for certain lattice models, demonstrated on a 2D anisotropic Heisenberg antiferromagnet.

Contribution

It develops a new operator-loop update within the stochastic series expansion framework, enhancing simulation efficiency for a broad class of lattice Hamiltonians.

Findings

Operator-loop method is more efficient than previous loop updates for some models.

The method is successfully tested on a 2D anisotropic Heisenberg antiferromagnet.

The approach is applicable to models with positive definite expansion.

Abstract

A cluster update (the ``operator-loop'') is developed within the framework of a numerically exact quantum Monte Carlo method based on the power series expansion of exp(-BH) (stochastic series expansion). The method is generally applicable to a wide class of lattice Hamiltonians for which the expansion is positive definite. For some important models the operator-loop algorithm is more efficient than loop updates previously developed for ``worldline'' simulations. The method is here tested on a two-dimensional anisotropic Heisenberg antiferromagnet in a magnetic field.