Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench

TL;DR

This paper demonstrates the existence of dynamical quantum phase transitions in two-dimensional strongly correlated spin lattices using a novel cumulant method, expanding understanding beyond one-dimensional models.

Contribution

The authors develop and apply a cumulant method to identify dynamical quantum phase transitions in 2D spin lattices, a significant advance over previous methods limited to one dimension.

Findings

Identified critical times in 2D quantum Ising and XYZ models.

Predicted dynamical phase transitions via initial energy fluctuations.

Extended analysis of quantum phase transitions to two-dimensional systems.

Abstract

Dynamical quantum phase transitions are at the forefront of current efforts to understand quantum matter out of equilibrium. Except for a few exactly solvable models, predictions of these critical phenomena typically rely on advanced numerical methods. However, those approaches are mostly restricted to one dimension, making investigations of two-dimensional systems highly challenging. Here, we present evidence of dynamical quantum phase transitions in strongly correlated spin lattices in two dimensions. To this end, we apply our recently developed cumulant method [Phys. Rev. X 11, 041018 (2021)] to determine the zeros of the Loschmidt amplitude in the complex plane of time and predict the crossing points of the thermodynamic lines of zeros with the real-time axis, where dynamical quantum phase transitions occur. We find the critical times of a two-dimensional quantum Ising lattice and the XYZ model with ferromagnetic or antiferromagnetic couplings. We also show how dynamical quantum phase transitions can be predicted by measuring the initial energy fluctuations, for example, in quantum simulators or other engineered quantum systems.