Scaling in driven dynamics starting in the vicinity of a quantum critical point

TL;DR

This paper develops a new scaling theory for driven quantum critical dynamics starting from near-critical equilibrium states, extending the Kibble-Zurek mechanism to include initial parameters and finite temperatures.

Contribution

It introduces a generalized scaling theory that accounts for initial conditions and finite-temperature effects in driven quantum critical dynamics.

Findings

Numerical simulations confirm the new scaling theory.

The theory applies to both zero and finite temperature initial states.

It extends the Kibble-Zurek mechanism to near-critical initial conditions.

Abstract

We study the driven critical dynamics with an equilibrium initial state near a quantum critical point. In contrast to the original Kibble-Zurek mechanism, which describes the driven dynamics starting from an adiabatic stage that is far from the critical point, the initial adiabacity is broken in this scenario. As a result, the scaling behavior cannot be described by the original Kibble-Zurek scaling. In this work we propose a scaling theory, which includes the initial parameters as additional scaling variables, to characterize the scaling behavior. In particular, this scaling theory can be used to describe the driven scaling behavior starting from a finite-temperature equilibrium state near a quantum critical point. We numerically confirm the scaling theory by simulating the real-time dynamics of the one-dimensional quantum Ising model at both zero and finite temperatures.