Wide sampling and efficient updating Monte Carlo algorithms for dimer models

TL;DR

This paper introduces an energy-directed loop Monte Carlo algorithm and improvements to the pocket algorithm for classical dimer models, significantly enhancing convergence speed and topological traversal efficiency.

Contribution

The paper presents a novel energy-directed loop updating algorithm and improved pocket algorithm for classical dimer models, outperforming traditional methods.

Findings

Energy directed loop algorithm increases convergence speed.

Improved algorithms reduce auto-correlation times.

Methods effectively traverse topological sectors.

Abstract

Quantum dimer model is a low-energy and efficient model to study quantum spin systems and strong-correlated physics. As a foreseeing step and without loss of generality, we study the classical dimers on square lattice by means of Monte Carlo method. For efficient states updating in dimer model, we introduce a highly-efficient loop updating algorithm directed by energy criterion called energy directed loop algorithm and improve the pocket algorithm to compare them with the traditional directed loop algorithm. By comparisons, our energy directed loop algorithm increases the convergent speed of Monte Carlo and shorten the auto-correlated time in classical hard-core dimer model. Both the improved pocket algorithm and energy path algorithm can be used in varietal dimer models and succeed in traversing the topological sections rapidly.