Quantum World-line Monte Carlo Method with Non-binary Loops and Its Application

TL;DR

This paper introduces a quantum world-line Monte Carlo method with non-binary loops for high-symmetry quantum models, demonstrating its effectiveness through numerical studies of SU(N) antiferromagnets.

Contribution

The paper presents a novel non-binary loop algorithm for quantum Monte Carlo simulations of SU(N) models, extending the applicability to high-symmetry systems.

Findings

Ground state for N <= 4 is Neel ordered.

Ground state for N >= 5 is a dimer state.

Algorithm successfully simulates high-symmetry quantum models.

Abstract

A quantum world-line Monte Carlo method for high-symmetrical quantum models is proposed. Firstly, based on a representation of a partition function using the Matsubara formula, the principle of quantum world-line Monte Carlo methods is briefly outlined and a new algorithm using non-binary loops is given for quantum models with high symmetry as SU(N). The algorithm is called non-binary loop algorithm because of non-binary loop updatings. Secondary, one example of our numerical studies using the non-binary loop updating is shown. It is the problem of the ground state of two-dimensional SU(N) anti-ferromagnets. Our numerical study confirms that the ground state in the small N <= 4 case is a magnetic ordered Neel state, but the one in the large N >= 5 case has no magnetic order, and it becomes a dimer state.