Floquet product mode and eigenphase order

TL;DR

This paper investigates the robustness of Floquet Majorana modes, especially the Floquet product mode, in a quantum Ising model under perturbations, linking their stability to spectral statistics of eigenphase quadruplets.

Contribution

It provides a novel analysis of Floquet edge modes using eigenphase order and spectral statistics, highlighting the enhanced robustness of the Floquet product mode.

Findings

Floquet eigenstates form quadruplets in the integrable limit.

Floquet product mode is more robust than individual Majorana modes.

Boundary spin correlations relate to spectral statistics of quadruplets.

Abstract

We study the robustness of the Floquet quantum Ising model against integrability-breaking perturbations, focusing on the phase hosting both Majorana zero and $\pi$ modes. A recent work [Phys. Rev. B 110, 075117, (2024)] observed that the Floquet product mode, a composite edge mode constructed from both Majorana operators, is considerably more robust than the individual Majorana edge modes. We analyze these strong modes from the point of view of the eigenphase order present in finite chains with open boundary conditions. As a result of the Majorana modes, all Floquet eigenstates come in quadruplets in the integrable limit. We show that the robustness of the various modes as well as the behavior of the boundary spin correlation functions can be understood in terms of the spectral statistics of these quadruplets in the presence of integrability-breaking perturbations.