Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions

Abstract

In non-Hermitian crystals showing the non-Hermitian skin effect, ordinary Bloch band theory and Bloch topological invariants fail to correctly predict energy spectra, topological boundary states, and symmetry breaking phase transitions in systems with open boundaries. Recently, it has been shown that a correct description requires to extend Bloch band theory into complex plane. A still open question is whether non-Hermitian skin effect and non-Bloch symmetry-breaking phase transitions can be probed by real-space wave dynamics far from edges, which is entirely governed by ordinary Bloch bands. Here it is shown that the Lyapunov exponent in the long-time behavior of bulk wave dynamics can reveal rather generally non-Bloch symmetry breaking phase transitions and the existence of the non-Hermitian skin effect.

14 pages, 8 figures, to appear in Physical Review Research

References in corpus (10)

• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Topological phase transition in non-Hermitian quasicrystals
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• New topological invariants in non-Hermitian systems
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Measurement of a topological edge invariant in a microwave network
• Nonadiabatic robust excitation transfer assisted by an imaginary gauge field

Cited by in corpus (225)

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• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
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• Helical damping and anomalous critical non-Hermitian skin effect
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• Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
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• Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System
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• Exact solution of single impurity problem in non-reciprocal lattices: impurity induced size-dependent non-Hermitian skin effect
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• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
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