Dynamics after a sweep through a quantum critical point

TL;DR

This paper investigates the non-equilibrium dynamics of a quantum many-body system after a critical point sweep, revealing complex scaling behaviors, entanglement properties, and relaxation phenomena beyond simple averages.

Contribution

It uncovers new scaling regimes and relaxation behaviors in the post-quench dynamics of a generalized quantum Ising model, including effects of integrability and non-integrability.

Findings

Two distinct entanglement entropy scaling regimes

Power-law relaxation of the Loschmidt echo

Absence of an effective temperature description

Abstract

The coherent quantum evolution of a one-dimensional many-particle system after sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and non-integrable regimes. It is known from previous work that universal power laws appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two scaling regimes of the entanglement entropy and a relaxation that is power-law rather than exponential. The final state of evolution after the quench is not well characterized by any effective temperature, and the Loschmidt echo converges algebraically to a constant for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.