Quantum Quench Dynamics in the Transverse Field Ising Model at Non-zero Temperatures

TL;DR

This paper investigates the effects of non-zero temperature on dynamical phase transitions in the transverse field Ising model, revealing that such transitions do not occur at finite temperatures due to thermal initial states.

Contribution

It extends the analysis of dynamical phase transitions to finite temperatures and shows their absence in the transverse field Ising model when T>0, using the generalized Loschmidt echo.

Findings

Dynamical phase transitions do not exist at T>0 in this model.

Features of zero-temperature non-analyticities are modified at finite temperature.

Tasaki-Crooks-Jarzynski relation can be used as a symmetry relation or to compute free energy changes.

Abstract

The recently discovered dynamical phase transition denotes non-analytic behavior in the real time evolution of quantum systems in the thermodynamic limit and has been shown to occur in different systems at zero temperature [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. In this paper we extend the analysis to non-zero temperature by studying a generalized form of the Loschmidt echo, the work distribution function, of a quantum quench in the transverse field Ising model. Although the quantitative behavior at non-zero temperatures still displays features derived from the zero temperature non-analyticities, it is shown that in this model dynamical phase transitions do not exist if $T>0$. This is a consequence of the system being initialized in a thermal state. Moreover, we elucidate how the Tasaki-Crooks-Jarzynski relation can be exploited as a symmetry relation for a global quench or to obtain the change of the equilibrium free energy density.