Why does bulk boundary correspondence fail in some non-hermitian topological models

By Ye Xiong. 2017

527 citations recorded by the source corpus.

The bulk-boundary correspondence is crucial to topological insulators. It associates the existence of boundary states (with zero energy and possessing chiral or helical properties) with the topological numbers defined in bulk. In recent years, topology has been extended to non-hermitian systems, opening a new research area called non-hermitian topological insulator. In this paper, however, we will illustrate that the bulk-boundary correspondence does not hold in these new models. This is because a prerequisite condition: ‘the boundaries cannot alter most of the bulk states, so as to the topological numbers defined on them’ does not hold any longer. This cuts out the correspondence between the topological numbers and the boundary states. We will illustrate that, as approaching the open boundary condition by eliminating the strength of the hopping between the two ends of a chain, a new series of exceptional points must be passed through and the topological structure of the spectrum in the complex plane has been changed. This makes the spectrum topology different for the chains with and without boundaries. We also discuss that such exotic behavior does not emerge when the open boundary is replaced by a domain-wall. So the index theorem can be applied to the systems with domain-walls but cannot be further used to those with open boundaries.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/031178889c680eb139210bccbfed25fa784dcbe2

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Non-Hermitian systems and topology: A transfer-matrix perspective (2018, methodology): “[45] Ye Xiong, “Why does bulk boundary correspondence fail in some non-Hermitian topological models,” Journal of Physics Communications 2, 035043 (2018).”
Higher-order non-Hermitian skin effect (2020, unknown): “[41] Y.”
Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems. (2018, background): “The paramount issue is the so-called non-Hermitian skin effect, meaning that a macroscopic number of left and right eigenmodes can pile up exponentially close to the boundary [13, 15, 23].”
Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices (2019, background): “, the nonreciprocal Su-Schrieffer-Heeger model [48, 49, 51, 53].”
A review on non-Hermitian skin effect (2022, background): “Contrary to the high sensitivity of EPs in the gain/loss-induced nonHermitian systems, recent studies have shown that EPs in nonreciprocityinduced non-Hermitian systems have strong fingerprints that can effectively pervade over a wide parameter regime and are possibly associated with the emergence o”
Edge States and Topological Invariants of Non-Hermitian Systems. (2018, unknown): “Recently, numerical results in a one-dimensional (1D) model show that open-boundary spectra look quite different from periodic-boundary ones, which seems to indicate a complete breakdown of bulk-boundary correspondence [49,86].”
Reciprocal skin effect and its realization in a topolectrical circuit (2019, background): “[17] Y.”
Topological Phases of Non-Hermitian Systems (2018, background): “[137] that an exponentially smallmodification of the boundary condition can lead to an order-one change in the spectrum.”