Path-integral Monte Carlo method for the local Z_2 Berry phase

TL;DR

This paper introduces a novel Monte Carlo loop cluster algorithm to compute the local Z_2 Berry phase in quantum spin models, effectively detecting quantum phase transitions and pinpointing critical points.

Contribution

It develops a new Monte Carlo method utilizing the meron cluster algorithm to accurately calculate the local Z_2 Berry phase in quantum spin systems.

Findings

Successfully detects valence bond pattern changes at quantum phase transitions

Demonstrates precise estimation of quantum critical points using the gauge-fixed local Berry connection

Validates the method on the antiferromagnetic Heisenberg model with bond alternation

Abstract

We present a loop cluster algorithm Monte Carlo method for calculating the local Z_2 Berry phase of the quantum spin models. The Berry connection, which is given as the inner product of two ground states with different local twist angles, is expressed as a Monte Carlo average on the worldlines with fixed spin configurations at the imaginary-time boundaries. The "complex weight problem" caused by the local twist is solved by adopting the meron cluster algorithm. We present the results of simulation on the antiferromagnetic Heisenberg model on an out-phase bond-alternating ladder to demonstrate that our method successfully detects the change in the valence bond pattern at the quantum phase transition point. We also propose that the gauge-fixed local Berry connection can be an effective tool to estimate pricisely the quantum critical point.