Unique and Universal scaling in dynamical quantum phase transitions

TL;DR

This paper reveals a universal power-law scaling of the critical time in dynamical quantum phase transitions, applicable across various systems and driven by the universality class, expanding understanding beyond equilibrium phase transitions.

Contribution

It uncovers a universal scaling law for critical time in dynamical quantum phase transitions, linking it to the universality class and validated in diverse quantum systems.

Findings

Critical time scales with quenching rate via a power law.

Scaling exponent determined by the universality class.

Universal behavior confirmed in both noninteracting and interacting systems.

Abstract

Universality and scaling are fundamental concepts in equilibrium continuous phase transitions. Here, we unveil a unique and universal scaling behavior of the critical time in slowly driven dynamical quantum phase transition. Going beyond the analogy with equilibrium phase transition, we find that the critical time exhibits a power-law scaling with quenching rate and the scaling exponent is fully determined by underlining universality class. We explain this unique scaling behavior based on the adiabatic-impulse scenario in the Kibble-Zurek mechanism. This universal scaling behavior is verified to be valid not only in noninteracting single-particle system, but also in many-body interacting system, and not only in Hermitian system, but also in non-Hermitian system. Our study unravels a deep and fundamental relationship between dynamical phase transition and equilibrium phase tranition.