Density of kinks after a sudden quench in the quantum Ising spin chain

TL;DR

This paper studies how the density of kinks evolves over time in a quantum Ising chain after a sudden change in the transverse field, revealing different relaxation behaviors at and away from criticality.

Contribution

It provides analytical insights into the long-time dynamics and the role of quantum criticality in the relaxation process of the quantum Ising model.

Findings

Density of kinks relaxes with oscillating power-law decay.

At criticality, residual kink density resembles a finite-temperature equilibrium state.

Outside criticality, the system does not thermalize.

Abstract

We investigate the time evolution of the density of kinks in the spin-1/2 quantum Ising spin chain after a sudden quench in the transverse field strength, and find that it relaxes to a value which depends on the initial and the final values of the transverse field, with an oscillating power-law decay. We provide analytical estimates of the long-time behavior and of the asymptotic value reached after complete relaxation, and discuss the role of quantum criticality in the quench dynamics. We show that, for a dynamics at the critical point, the residual density of kinks after the quench can be described by equilibrium statistical mechanics at a finite temperature dictated by the energy of the state after the quench. On the other hand, outside of criticality it does not exhibit thermalization.