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

Abstract

This paper demonstrates that the ground state subspace of systems with topological order - such as the toric code and systems with fracton order - can stay real under a robust set of non-Hermitian perturbations. This preservation of the reality of eigenvalues is sensitive to the size of the system, the conditions for which can be formulated both algebraically and geometrically.