Finite-Temperature Dynamical Phase Diagram of the $2+1$D Quantum Ising Model

TL;DR

This paper introduces an efficient quantum Monte Carlo approach to map the finite-temperature dynamical phase diagram of the 2+1D quantum Ising model, revealing novel quenches and phase transitions without simulating full unitary dynamics.

Contribution

The authors develop a new equilibrium QMC method leveraging energy conservation to determine late-time observables, enabling the study of dynamical phases at finite temperatures.

Findings

Identification of quenches that cool the system in the ordered phase

Discovery of initial temperature intervals allowing PM to FM quenches

Proposal for quantum simulation experiments to observe dynamical phases

Abstract

Mapping finite-temperature dynamical phase diagrams of quantum many-body models is a necessary step towards establishing a framework of far-from-equilibrium quantum many-body universality. However, this is quite difficult due, in part, to the severe challenges in representing the volume-law entanglement that is generated under nonequilibrium dynamics at finite temperatures. Here, we address these challenges with an efficient equilibrium quantum Monte Carlo (QMC) framework for computing the finite-temperature dynamical phase diagram. Our method uses energy conservation and the self-thermalizing properties of ergodic quantum systems to determine observables at late times after a quantum quench. We use this technique to chart the dynamical phase diagram of the $2+1$D quantum Ising model generated by quenches of the transverse field in initial thermal states. Our approach allows us to track the evolution of dynamical phases as a function of both the initial temperature and transverse field. Surprisingly, we identify quenches in the ordered phase that cool the system as well as an interval of initial temperatures where it is possible to quench from the paramagnetic (PM) to ferromagnetic (FM) phases. Our method gives access to dynamical properties without explicitly simulating unitary time evolution, and is immediately applicable to other lattice geometries and interacting many-body systems. Finally, we propose a quantum simulation experiment on state-of-the-art digital quantum hardware to directly probe the predicted dynamical phases and their real-time formation.