Solving quantum rotor model with different Monte Carlo techniques

TL;DR

This paper compares various Monte Carlo techniques for simulating the quantum rotor model at criticality, identifying the most efficient schemes in terms of autocorrelation and computational cost, with implications for complex quantum systems.

Contribution

It systematically evaluates and compares multiple Monte Carlo update schemes for the quantum rotor model, highlighting the efficiency of Wolff-cluster and Fourier acceleration methods.

Findings

Wolff-cluster and Fourier acceleration schemes have the lowest autocorrelation times.

These schemes require less CPU time to achieve the same error levels.

Fourier acceleration is adaptable to more complex interactions.

Abstract

We systematically test the performance of several Monte Carlo update schemes for the $(2+1)$d XY phase transition of quantum rotor model. By comparing the local Metropolis (LM), LM plus over-relaxation (OR), Wolff-cluster (WC), hybrid Monte Carlo (HM), hybrid Monte Carlo with Fourier acceleration (FA) scheme, it is clear that among the five different update schemes, at the quantum critical point, the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error, and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones. These results bestow one with the necessary knowledge of extending the quantum rotor model, which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z$_2$ topological order, to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.