Cluster Monte Carlo Algorithm for the Quantum Rotor Model

TL;DR

This paper introduces an efficient cluster Monte Carlo algorithm for the quantum rotor model, providing high-precision estimates of critical points and exponents for both pure and disordered cases.

Contribution

A new worm-like cluster Monte Carlo algorithm is developed for the quantum rotor model, with proven detailed balance and improved accuracy in critical parameter estimation.

Findings

High-precision critical point estimate: $K_c=0.33305(5)$

Correlation length exponent for pure case: $ u=0.670(3)$

Disordered case exponent: $ u=1.15(10)

Abstract

We propose a highly efficient "worm" like cluster Monte Carlo algorithm for the quantum rotor model in the link-current representation. We explicitly prove detailed balance for the new algorithm even in the presence of disorder. For the pure quantum rotor model with $\mu=0$ the new algorithm yields high precision estimates for the critical point $K_c=0.33305(5)$ and the correlation length exponent $\nu=0.670(3)$. For the disordered case, $\mu=1/2 \pm 1/2$, we find $\nu=1.15(10)$.