Spin chain simulations with a meron cluster algorithm

TL;DR

This paper demonstrates the application of a meron cluster algorithm to simulate the XY spin chain with a theta-term, enabling precise numerical results for a complex action system and highlighting its efficiency and potential for higher-dimensional models.

Contribution

The paper introduces a multi-cluster meron algorithm with an improved estimator for the XY spin chain, effectively handling objects with half-integer topological charge and solving a complex action system numerically.

Findings

Accurate measurement of correlation length, topological, and magnetic susceptibilities.

The algorithm effectively mitigates critical slowing down.

Strong performance suggests applicability to higher-dimensional models.

Abstract

We apply a meron cluster algorithm to the XY spin chain, which describes a quantum rotor. This is a multi-cluster simulation supplemented by an improved estimator, which deals with objects of half-integer topological charge. This method is powerful enough to provide precise results for the model with a theta-term - it is therefore one of the rare examples, where a system with a complex action can be solved numerically. In particular we measure the correlation length, as well as the topological and magnetic susceptibility. We discuss the algorithmic efficiency in view of the critical slowing down. Due to the excellent performance that we observe, it is strongly motivated to work on new applications of meron cluster algorithms in higher dimensions.