Universal anti-Kibble-Zurek scaling in fully-connected systems

TL;DR

This paper reveals a universal anti-Kibble-Zurek scaling law in open fully-connected quantum systems, showing that slower quenches can increase non-adiabatic effects due to environment interactions, contrary to isolated system predictions.

Contribution

It demonstrates that anti-Kibble-Zurek scaling can be universal in open systems, governed by equilibrium critical exponents, in contrast to previous non-universal observations.

Findings

Universal anti-Kibble-Zurek scaling law identified

Scaling determined by equilibrium critical exponents

Validated in quantum Rabi and Lipkin-Meshkov-Glick models

Abstract

We investigate the quench dynamics of an open quantum system involving a quantum phase transition. In the isolated case, the quench dynamics involving the phase transition exhibits a number of scaling relations with the quench rate as predicted by the celebrated Kibble-Zurek mechanism. In contact with an environment however, these scaling laws breakdown and one may observe an anti-Kibble-Zurek behavior: slower ramps lead to less adiabatic dynamics, increasing thus non-adiabatic effects with the quench time. In contrast to previous works, we show here that such anti-Kibble-Zurek scaling can acquire a universal form in the sense that it is determined by the equilibrium critical exponents of the phase transition, provided the excited states of the system exhibit singular behavior, as observed in fully-connected models. This demonstrates novel universal scaling laws granted by a system-environment interaction in a critical system. We illustrate these findings in two fully-connected models, namely, the quantum Rabi and the Lipkin-Meshkov-Glick models. In addition, we discuss the impact of non-linear ramps and finite-size systems.