Quantum phase transition dynamics in the two-dimensional transverse-field Ising model

TL;DR

This paper investigates the dynamics of quantum phase transitions in the two-dimensional transverse-field Ising model, extending the quantum Kibble-Zurek mechanism to higher dimensions using advanced numerical methods.

Contribution

It presents the first theoretical exploration of the quantum Kibble-Zurek mechanism in two-dimensional quantum matter, incorporating neural networks and tensor networks.

Findings

Quantifies universal QKZM behavior near the QPT

Identifies deviations from QKZM in the ferromagnetic regime

Proposes an extended QKZM incorporating spectral and phase information

Abstract

The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical behavior near the quantum phase transitions (QPTs). It is now well understood for the one-dimensional quantum matter. Higher-dimensional systems, however, remain a challenge, complicated by the fundamentally different character of the associated QPTs and their underlying conformal field theories. In this work, we take the first steps toward theoretical exploration of the QKZM in two dimensions for interacting quantum matter. We study the dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort of modern state-of-the-art numerical methods, including artificial neural networks and tensor networks. As a central result, we quantify universal QKZM behavior close to the QPT. We also note that, upon traversing further into the ferromagnetic regime, deviations from the QKZM prediction appear. We explain the observed behavior by proposing an {\it extended QKZM} taking into account spectral information as well as phase ordering. Our work provides a testing platform for higher-dimensional quantum simulators.