Kibble-Zurek scaling from linear response theory

TL;DR

This paper demonstrates that linear response theory and the Kibble-Zurek mechanism are consistent in describing non-equilibrium dynamics of quantum phase transitions, providing a rigorous basis for their application.

Contribution

It shows that linear response theory can inform and support the Kibble-Zurek mechanism in quantum phase transitions, establishing their compatibility and extending their applicability.

Findings

Linear response theory provides a relaxation time consistent with the Kibble-Zurek gap.

Excess work computed from linear response exhibits Kibble-Zurek scaling.

The approaches are shown to be compatible in describing quantum critical dynamics.

Abstract

While quantum phase transitions share many characteristics with thermodynamic phase transitions, they are also markedly different as they occur at zero temperature. Hence, it is not immediately clear whether tools and frameworks that capture the properties of thermodynamic phase transitions also apply in the quantum case. Concerning the crossing of thermodynamic critical points and describing its non-equilibrium dynamics, the Kibble-Zurek mechanism and linear response theory have been demonstrated to be among the very successful approaches. In the present work, we show that these two approaches are consistent also in the description of quantum phase transitions, and that linear response theory can even inform arguments of the Kibble-Zurek mechanism. In particular, we show that the relaxation time provided by linear response theory gives a rigorous argument for why to identify the "gap" as a relaxation rate, and we verify that the excess work computed from linear response theory exhibits Kibble-Zurek scaling.