Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models

TL;DR

This paper establishes criteria for protecting $ ext{-}T$-symmetry in topological many-body systems, demonstrating robustness of real eigenvalues under non-Hermitian perturbations in models like the toric code and fracton systems.

Contribution

It provides simple geometric and algebraic criteria for $ ext{-}T$-symmetry protection in topological systems, with demonstrations on toric code and fracton models.

Findings

$ ext{-}T$-symmetry is robust against many non-Hermitian perturbations

Eigenvalues remain real under broad classes of perturbations

Protection is especially notable in fracton models with large degeneracy

Abstract

In the study of $\mathcal{P}\mathcal{T}$-symmetric quantum systems with non-Hermitian perturbations, one of the most important questions is whether eigenvalues stay real or whether $\mathcal{P}\mathcal{T}$-symmetry is spontaneously broken when eigenvalues meet. A particularly interesting set of eigenstates is provided by the degenerate ground-state subspace of systems with topological order. In this paper, we present simple criteria that guarantee the protection of $\mathcal{P}\mathcal{T}$-symmetry and, thus, the reality of the eigenvalues in topological many-body systems. We formulate these criteria in both geometric and algebraic form, and demonstrate them using the toric code and several different fracton models as examples. Our analysis reveals that $\mathcal{P}\mathcal{T}$-symmetry is robust against a remarkably large class of non-Hermitian perturbations in these models; this is particularly striking in the case of fracton models due to the exponentially large number of degenerate states.