Eigenvalue-flipping Algorithm for Matrix Monte Carlo

TL;DR

This paper introduces an improved Monte Carlo algorithm for large matrix models that enables efficient tunneling between different vacua by externally controlling eigenvalue sign changes, demonstrated on specific models.

Contribution

The paper presents a novel eigenvalue-flipping algorithm that enhances ergodicity in matrix Monte Carlo simulations for large models, addressing a key limitation of existing methods.

Findings

Effective tunneling between vacua demonstrated

Algorithm successfully applied to matrix potential and fuzzy sphere models

Improved ergodicity in large matrix Monte Carlo simulations

Abstract

Many physical systems can be described in terms of matrix models that we often cannot solve analytically. Fortunately, they can be studied numerically in a straightforward way. Many commonly used algorithms follow the Monte Carlo method, which is efficient for small matrix sizes but cannot guarantee ergodicity when working with large ones. In this paper, we propose an improvement of the algorithm that, for a large class of matrix models, allows to tunnel between various vacua in a proficient way, where sign change of eigenvalues is proposed externally. We test the method on two models: the pure potential matrix model and the scalar field theory on the fuzzy sphere.