Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model

TL;DR

This paper investigates the phases and dynamics of a nonunitary Floquet transverse-field Ising model, revealing stable phases with edge modes, long-range order, and complex entanglement scaling, extending understanding of non-Hermitian quantum systems.

Contribution

It introduces a detailed analysis of nonunitary Floquet Ising models, highlighting new steady phases, entanglement behaviors, and the role of pseudo-Hermiticity in phase transitions.

Findings

Existence of stable phases with edge modes and long-range order.

Entanglement entropy exhibits volume law scaling on critical lines.

Quasiparticle picture extends to non-Hermitian dynamics, explaining entanglement scaling.

Abstract

Inspired by current research on measurement-induced quantum phase transitions, we analyze the nonunitary Floquet transverse-field Ising model with complex nearest-neighbor couplings and complex transverse fields. Unlike its unitary counterpart, the model shows a number of steady phases, stable to integrability breaking perturbations. Some phases have robust edge modes and/or spatiotemporal long-range orders in the bulk. The transitions between the phases have extensive entanglement entropy, whose scaling with the system size depends on the number of the real quasiparticle modes in the spectrum at the transition. In particular, the volume law scaling appears on some critical lines, protected by pseudo-Hermiticity. Both the scaling of entanglement entropy in steady states and the evolution after a quench are compatible with the non-Hermitian generalization of the quasiparticle picture of Calabrese and Cardy at least qualitatively.