Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk

Abstract

Non-Hermitian systems exhibit richer topological properties compared to their Hermitian counterparts. It is well known that non-Hermitian systems have been classified based on either the symmetry relations for non-Hermitian Hamiltonians or the symmetry relations for non-unitary time-evolution operators in the context of Floquet topological phases. In this work, we propose that non-Hermitian systems can always be classified in two ways; a non-Hermitian system can be classified using the symmetry relations for non-Hermitian Hamiltonians or time-evolution operator regardless of the Floquet topological phases or not. We refer to this as dual symmetry classification. To demonstrate this, we successfully introduce a new non-unitary quantum walk that exhibits point gaps with a ${\mathbb{Z}}_2$ point-gap topological phase applying the dual symmetry classification and treating the time-evolution operator of this quantum walk as the non-Hermitian Hamiltonian.

10 pages, 8 figures

References in corpus (15)

• Topological Origin of Non-Hermitian Skin Effects
• Universal non-Hermitian skin effect in two and higher dimensions
• Non-Hermitian topological phenomena: A review
• Observation of higher-order non-Hermitian skin effect
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Optimizing the discrete time quantum walk using a SU(2) coin
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Non-Hermitian skin effect beyond the tight-binding models
• Hermitian and Non-Hermitian Topology from Photon-Mediated Interactions
• Non-Hermitian skin effect edge
• Topological enhancement of non-normality in non-Hermitian skin effects
• Photon and phonon statistics in a qubit-plasmon-phonon ultrastrong coupling system
• Multi-Dimensional Quantum Walks: a Playground of Dirac and Schrödinger Particles
• Bulk-Edge Correspondence for Point-Gap Topological Phases in Junction Systems

Cited by in corpus (4)

• Proposal of a quantum version of active particles via a nonunitary quantum walk
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Origin of Robust ${\mathbb{Z}}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion
• Two-Polariton Blockade via Ultrastrong Light-Matter Coupling