Topological Phase Transitions of Generalized Brillouin Zone

Abstract

It has been known that the bulk-boundary correspondence (BBC) of the non-Hermitian skin effect is characterized by the topology of the complex eigenvalue spectra, while the topology of the wave function gives rise to Hermitian BBC with conventional boundary modes. In this work, we go beyond the known description of the non-Hermitian topological phase by discovering a new type of BBC that appears in generalized boundary conditions. The generalized Brillouin zone (GBZ) possesses non-trivial topological structures in the intermediate boundary condition between open and periodic boundary conditions. Unlike the conventional BBC, the topological phase transition is characterized by the generalized momentum touching of GBZ, which manifests as exceptional points. As a realization of our proposal, we suggest the non-reciprocal Kuramoto oscillator lattice, where the phase slips accompany the exceptional points as a signature of such topological phase transition. Our work establishes an understanding of non-Hermitian topological matter by complementing the non-Hermitian BBC as a general foundation of the non-Hermitian topological systems.

43 pages, 23 figures

References in corpus (4)

• Topological Origin of Non-Hermitian Skin Effects
• Non-Hermitian topological phenomena: A review
• Topological active matter
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect

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• Bulk-boundary correspondence in extended trimer Su-Schrieffer-Heeger model
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Adiabatic charge transport through non-Bloch bands
• Topology of the generalized Brillouin zone of one-dimensional models
• 1D Spontaneous Symmetry Breaking in thermal equilibrium via Non-Hermitian Construction
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems