Dynamical Triplet Unravelling: A quantum Monte Carlo algorithm for reversible dynamics

TL;DR

This paper presents a novel quantum Monte Carlo algorithm that enables simulation of reversible dynamics in correlated many-body systems over longer timescales by utilizing the Laplace transform and a deadweight approximation.

Contribution

The authors introduce a new quantum Monte Carlo method based on Laplace transforms and deadweight approximation to efficiently simulate long-time reversible dynamics in many-body quantum systems.

Findings

Successfully simulated spin excitation propagation in the XXZ model.

Analyzed dynamical confinement in the quantum Ising chain.

Demonstrated stabilization of many-body phases at longer times.

Abstract

We introduce a quantum Monte Carlo method to simulate the reversible dynamics of correlated many-body systems. Our method is based on the Laplace transform of the time-evolution operator which, as opposed to most quantum Monte Carlo methods, makes it possible to access the dynamics at longer times. The Monte Carlo trajectories are realised through a piece-wise stochastic-deterministic reversible evolution where free dynamics is interspersed with two-process quantum jumps. The dynamical sign problem is bypassed via the so-called deadweight approximation, which stabilizes the many-body phases at longer times. We benchmark our method by simulating spin excitation propagation in the XXZ model and dynamical confinement in the quantum Ising chain, and show how to extract dynamical information from the Laplace representation.