Non-equilibrium variational cluster perturbation theory: quench dynamics of the quantum Ising model

TL;DR

This paper develops a variational cluster perturbation theory to simulate non-equilibrium dynamics in quantum spin systems, accurately capturing real-time evolution after quenches in the quantum Ising model.

Contribution

It introduces a novel variational CPT method for non-equilibrium spin dynamics and benchmarks it against exact solutions in the quantum Ising model.

Findings

Method accurately describes dynamics up to a certain time scale

Time scale increases with cluster size

Quench type affects the characteristic time scale

Abstract

We introduce a variational implementation of cluster perturbation theory (CPT) to address the dynamics of spin systems driven out of equilibrium. We benchmark the method with the quantum Ising model subject to a sudden quench of the transverse magnetic field across the transition or within a phase. We treat both the one-dimensional case, for which an exact solution is available, as well the two-dimensional one, for which has to resort to numerical results. Comparison with exact results shows that the approach provides a quite accurate description of the real-time dynamics up to a characteristic time scale $\tau$ that increses with the size of the cluster used for CPT. In addition, and not surprisingly $\tau$ is small for quenches across the equilibrium phase transition, but can be quite larger for quenches within the ordered or disordered phases.