Quantum Monte Carlo simulation of spin-boson models using wormhole updates

TL;DR

This paper introduces an exact quantum Monte Carlo method with nonlocal wormhole updates for simulating spin-boson models, enabling precise analysis of phase transitions in dissipative quantum systems.

Contribution

The paper develops a novel quantum Monte Carlo algorithm using wormhole updates that extends global moves to nonlocal configurations, applicable to a wide range of spin-boson models.

Findings

Accurately estimates the critical coupling in a two-bath spin-boson model.

Demonstrates the method's applicability to impurity and lattice systems in any dimension.

Provides a precise phase boundary between critical and localized phases.

Abstract

We present an exact quantum Monte Carlo method for spin systems coupled to dissipative bosonic baths which makes use of nonlocal wormhole updates to simulate the retarded spin-flip interactions originating from an off-diagonal spin-boson coupling. The method is closely related to the stochastic series expansion and extends the scope of the global directed-loop updates to nonlocal moves through a world-line configuration. We test our method for the U(1)-symmetric two-bath spin-boson model, where the off-diagonal components of a spin-$1/2$ particle are coupled to identical independent baths with power-law spectra, and get a precise estimate of the critical coupling between the critical and the localized phase. Our method applies to impurity systems and lattice models in any spatial dimension coupled to bosonic modes with arbitrary spectral distributions.