Kibble-Zurek scaling due to environment temperature quench in the transverse field Ising model

TL;DR

This paper investigates how defect density scales during a temperature quench through a critical point in the transverse field Ising model, revealing modified Kibble-Zurek scaling due to environment interactions.

Contribution

It introduces a novel analysis of Kibble-Zurek scaling under thermal environment quenches, extending understanding to dissipative quantum systems with bath interactions.

Findings

Defect density scales as τ^{-dν} or τ^{-d/z} depending on the critical point type.

Enhanced relaxation reduces defect density compared to traditional Kibble-Zurek predictions.

Scaling laws are confirmed via Lindblad equation simulations for the transverse field Ising chain.

Abstract

The Kibble-Zurek mechanism describes defect production due to non-adiabatic passage through a critical point. Here we study its variant from ramping the environment temperature to a critical point. We find that the defect density scales as $\tau^{-d\nu}$ or $\tau^{-d/z}$ for thermal or quantum critical points, respectively, in terms of the usual critical exponents and $1/\tau$ the speed of the drive. Both scalings describe reduced defect density compared to conventional Kibble-Zurek mechanism, which stems from the enhanced relaxation due to bath-system interaction. Ramping to the quantum critical point is investigated by studying the Lindblad equation for the transverse field Ising chain in the presence of thermalizing bath, with couplings to environment obeying detailed balance, confirming the predicted scaling. The von-Neumann or the system-bath entanglement entropy follows the same scaling. Our results are generalized to a large class of dissipative systems with power-law energy dependent bath spectral densities as well.