A quantum Monte Carlo algorithm realizing an intrinsic relaxation

TL;DR

This paper introduces a novel quantum Monte Carlo algorithm that accurately captures intrinsic relaxation in quantum systems, independent of Trotter number, and is validated on the 2D transverse-field Ising model.

Contribution

A new quantum Monte Carlo algorithm combining local and cluster flips that realizes true system relaxation and is independent of Trotter discretization effects.

Findings

The algorithm satisfies the dynamic scaling relation τ∼ξ^z.

It enables observation of true relaxation in the original quantum system.

An accurate phase diagram for the 2D transverse-field Ising model was obtained.

Abstract

We propose a new quantum Monte Carlo algorithm which realizes a relaxation intrinsic to the original quantum system. The Monte Carlo dynamics satisfies the dynamic scaling relation $\tau\sim \xi^z$ and is independent of the Trotter number. Finiteness of the Trotter number just appears as the finite-size effect. An infinite Trotter number version of the algorithm is also formulated, which enables us to observe a true relaxation of the original system. The strategy of the algorithm is a compromise between the conventional worldline local flip and the modern cluster loop flip. It is a local flip in the real-space direction and is a cluster flip in the Trotter direction. The new algorithm is tested by the transverse-field Ising model in two dimensions. An accurate phase diagram is obtained.