Dynamical Quantum Phase Transitions in the Transverse Field Ising Model

TL;DR

This paper investigates dynamical phase transitions in the transverse field Ising model, revealing non-analytic behavior at critical times during quantum evolution, analogous to temperature-driven phase transitions.

Contribution

It demonstrates the existence of dynamical phase transitions in the transverse field Ising model and links them to equilibrium quantum phase transitions.

Findings

Identification of non-analytic behavior at critical times

Relation between equilibrium and dynamical phase transitions

Insights into real-time quantum system evolution

Abstract

A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this paper we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely non-analytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse field Ising model. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related.