Hybridized Kibble-Zurek scaling in the driven critical dynamics across an overlapping critical region

TL;DR

This paper introduces a hybridized Kibble-Zurek scaling (HKZS) to describe the driven critical dynamics in overlapping critical regions, validated through numerical simulations of a quantum Ising chain with overlapping phase transition regions.

Contribution

The paper develops and validates a new HKZS framework for analyzing driven dynamics across overlapping critical regions, extending traditional Kibble-Zurek scaling.

Findings

HKZS describes simultaneous critical theories in overlapping regions

Numerical confirmation in quantum Ising chain model

Applicable to other models with overlapping critical regions

Abstract

The conventional Kibble-Zurek scaling describes the scaling behavior in the driven dynamics across a single critical region. In this paper, we study the driven dynamics across an overlapping critical region, in which a critical region (Region-A) is overlaid by another critical region (Region-B). We develop a hybridized Kibble-Zurek scaling (HKZS) to characterize the scaling behavior in the driven process. According to the HKZS, the driven dynamics in the overlapping region can be described by the critical theories for both Region-A and Region-B simultaneously. This results in a constraint on the scaling function in the overlapping critical region. We take the quantum Ising chain in an imaginary longitudinal-field as an example. In this model, the critical region of the Yang-Lee edge singularity and the critical region of the ferromagnetic-paramagnetic phase transition point overlap with each other. We numerically confirm the HKZS by simulating the driven dynamics in this overlapping region. The HKZSs in other models are also discussed.