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

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.

20 pages, 6 figures

References in corpus (28)

• Making Sense of Non-Hermitian Hamiltonians
• Exceptional Topology of Non-Hermitian Systems
• The physics of exceptional points
• Loss-induced suppression and revival of lasing
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Local stabilizer codes in three dimensions without string logical operators
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Topological phase transition in non-Hermitian quasicrystals
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Fracton Phases of Matter
• Optomechanically-Induced Transparency in partiy-time-symmetric microresonators
• Entanglement and spin squeezing in non-Hermitian phase transitions
• Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Nonunitary Scaling Theory of Non-Hermitian Localization
• Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
• Emergent Fermi surface in a many-body non-Hermitian Fermionic chain
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Topological states in non-Hermitian two-dimensional Su-Schrieffer-Heeger model
• Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices
• Non-Hermitian BCS-BEC evolution with a complex scattering length
• Quantum transport in non-Hermitian impurity array
• Direct observation of energy band attraction effect in non-Hermitian systems
• Balanced gain and loss in spatially extended non-$\mathcal{P}\mathcal{T}$-symmetric multi-well potentials

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• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Many-body localization in a non-Hermitian quasi-periodic system
• Many-body topology of non-Hermitian systems
• Foliated Quantum Field Theory of Fracton Order
• Exceptional Spin Liquids from Couplings to the Environment
• Non-Hermitian Mott Skin Effect
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Dynamical robustness of topological end states in nonreciprocal Su-Schrieffer-Heeger models with open boundary conditions
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• Non-Hermitian dynamics and $\mathcal{P}\mathcal{T}$-symmetry breaking in interacting mesoscopic Rydberg platforms
• Dynamical scaling of Loschmidt echo in non-Hermitian systems
• High-order series expansion of non-Hermitian quantum spin models
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Correlation effects on non-Hermitian point-gap topology in zero dimension: reduction of topological classification
• Multifractality of many-body non-Hermitian skin effect
• Quantum fluctuations on top of a $\mathcal{P}\mathcal{T}$-symmetric Bose-Einstein Condensate
• Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation
• Kondo effect in a non-Hermitian, $\mathcal{P}\mathcal{T}$-symmetric Anderson model with Rashba spin-orbit coupling
• Mixedness timescale in non-Hermitian quantum systems