Quantum criticality at the boundary of the non-Hermitian regime of a Floquet system

TL;DR

This paper explores quantum criticality at the boundary of non-Hermitian regimes in a Floquet system, revealing a transition in quantum scrambling dynamics characterized by out-of-time ordered correlators.

Contribution

It provides analytical and numerical insights into the quantum critical behavior of a non-Hermitian quantum kicked rotor at resonance conditions.

Findings

Transition from linear to quadratic growth in OTOCs at critical point

Divergence of growth rates indicating quantum criticality

Analytical expressions for OTOCs as a function of time

Abstract

We investigate both analytically and numerically the dynamics of quantum scrambling, characterized by the out-of-time ordered correlators (OTOCs), in a non-Hermitian quantum kicked rotor subject to quantum resonance conditions. Analytical expressions for OTOCs as a function of time are obtained, demonstrating a sudden transition from the linear growth to quadratic growth when the non-Hermitian parameter decays to zero. At this critical point, the rates of the linear growth are found to diverge to infinity, indicating the existence of quantum criticality at the boundary of the non-Hermitian regime. The underlying mechanism of this quantum criticality is uncovered, and possible applications in quantum metrology are discussed.