Monte Carlo simulation with aspect ratio optimization: Anomalous anisotropic scaling in dimerized antiferromagnet

TL;DR

This paper introduces an aspect ratio optimization method for quantum Monte Carlo simulations that automatically adjusts anisotropic lattice models to be effectively isotropic, improving universality analysis.

Contribution

The paper presents a novel Robbins-Monro based approach to optimize lattice aspect ratios during quantum Monte Carlo simulations, enabling more accurate universality comparisons.

Findings

Optimized aspect ratio reduces size corrections in simulations.

Identified strong size effects due to cubic interactions.

Clarified non-universal behavior in dimerized antiferromagnets.

Abstract

We present a method that optimizes the aspect ratio of a spatially anisotropic quantum lattice model during the quantum Monte Carlo simulation, and realizes the virtually isotropic lattice automatically. The anisotropy is removed by using the Robbins-Monro algorithm based on the correlation length in each direction. The method allows for comparing directly the value of critical amplitude among different anisotropic models, and identifying the universality more precisely. We apply our method to the staggered dimer antiferromagnetic Heisenberg model and demonstrate that the apparent non-universal behavior is attributed mainly to the strong size correction of the effective aspect ratio due to the existence of the cubic interaction.