Non-invertible symmetries out of equilibrium

TL;DR

This paper explores how non-invertible symmetries influence the dynamics of disordered quantum systems, revealing spectral degeneracies, SPT order distinctions, and edge mode behaviors, including Floquet-driven period doubling.

Contribution

It demonstrates the manifestation of non-invertible symmetries in out-of-equilibrium dynamics and introduces a Floquet model exhibiting novel edge mode phenomena.

Findings

Spectral degeneracies scale with system size due to non-invertible symmetry.

Eigenstates show distinct SPT orders detectable via string order parameters.

Edge modes oscillate with temperature-dependent frequencies and exhibit period doubling in Floquet systems.

Abstract

Through the study of the Rep($D_8$) non-invertible symmetry, we show how non-invertible symmetries manifest in dynamics. By considering the effect of symmetry preserving disorder, the non-invertible symmetry is shown to give rise to degeneracies in the spectra that can only be completely lifted at orders of perturbation that scale with system size. The eigenstates of disordered Hamiltonians, whose ground state correspond to non-trivial symmetry protected topological (SPT) states, are shown to have either trivial or non-trivial SPT order that are detected as non-zero expectation value of string order-parameters. In contrast, non-trivial SPT order is absent in the eigenstates of trivial SPT Hamiltonians with disorder. The interface between two different SPT phases host edge modes whose dynamics is studied numerically and analytically. The edge mode is shown to oscillate at frequencies related to different effective chain lengths that are weighted by the temperature, becoming an exact zero mode in the limit of zero temperature. A Floquet model with the non-invertible symmetry is constructed whose edge mode is shown to exhibit period-doubled dynamics at low effective-temperatures.