Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition

TL;DR

This study investigates the non-equilibrium dynamics of a long-range transverse-field Ising model, revealing a long-lived prethermal regime with persistent order and a dynamical phase transition distinct from equilibrium behavior.

Contribution

It demonstrates the existence of a prethermal regime with persistent order in a long-range quantum Ising model, even without a finite-temperature phase transition in equilibrium.

Findings

Identification of a long-lived prethermal magnetization regime.

Observation of a dynamical phase transition between symmetry-broken and symmetric phases.

The dynamical critical point shifts depending on the interaction range and quench parameters.

Abstract

We numerically study the dynamics after a parameter quench in the one-dimensional transverse-field Ising model with long-range interactions ($\propto 1/r^\alpha$ with distance $r$), for finite chains and also directly in the thermodynamic limit. In nonequilibrium, i.e., before the system settles into a thermal state, we find a long-lived regime that is characterized by a prethermal value of the magnetization, which in general differs from its thermal value. We find that the ferromagnetic phase is stabilized dynamically: as a function of the quench parameter, the prethermal magnetization shows a transition between a symmetry-broken and a symmetric phase, even for those values of $\alpha$ for which no finite-temperature transition occurs in equilibrium. The dynamical critical point is shifted with respect to the equilibrium one, and the shift is found to depend on $\alpha$ as well as on the quench parameters.