Boundary-sensitive non-Hermiticity of Floquet Hamiltonian: spectral transition and scale-free localization

TL;DR

This paper introduces a boundary-sensitive PT symmetry breaking mechanism in Floquet systems, revealing a transition driven by quasienergy bandwidth expansion and resulting in scale-free localization of eigenstates.

Contribution

It presents a novel Floquet engineering approach to induce boundary-sensitive non-Hermitian effects and characterizes the associated spectral transition and localization phenomena.

Findings

PT symmetry breaking occurs when quasienergy bandwidth covers the entire Brillouin zone

Eigenstates show scale-free localization in the PT-broken phase

A general framework for multi-band models with boundary-induced transitions

Abstract

We report a novel mechanism of boundary-sensitive PT symmetry breaking in one-dimensional Floquet systems. By designing a time-periodic driving protocol, we realize a Floquet Hamiltonian that is Hermitian under periodic boundary conditions yet acquires non-Hermitian boundary terms under open boundary conditions due to the non-commutativity of driving Hamiltonians. We establish that a PT symmetry breaking transition occurs when the quasienergy bandwidth expands to cover the entire frequency Brillouin zone. This condition highlights a crucial difference from static non-Hermitian systems, where such transitions typically require band touching. Furthermore, we demonstrate that in the PT-broken phase, the eigenstates exhibit scale-free localization, a phenomenon arising from the specific system-size scaling of non-Hermitian terms. Finally, we provide a general framework for constructing multi-band models that exhibit this boundary-induced phase transition.