Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems.

By Flore K. Kunst, Elisabet Edvardsson, J. C. Budich, E. Bergholtz. Physical Review Letters, 2018

1,050 citations recorded by the source corpus.

Non-Hermitian systems exhibit striking exceptions from the paradigmatic bulk-boundary correspondence, including the failure of bulk Bloch band invariants in predicting boundary states and the (dis)appearance of boundary states at parameter values far from those corresponding to gap closings in periodic systems without boundaries. Here, we provide a comprehensive framework to unravel this disparity based on the notion of biorthogonal quantum mechanics: While the properties of the left and right eigenstates corresponding to boundary modes are individually decoupled from the bulk physics in non-Hermitian systems, their combined biorthogonal density penetrates the bulk precisely when phase transitions occur. This leads to generalized bulk-boundary correspondence and a quantized biorthogonal polarization that is formulated directly in systems with open boundaries. We illustrate our general insights by deriving the phase diagram for several microscopic open boundary models, including exactly solvable non-Hermitian extensions of the Su-Schrieffer-Heeger model and Chern insulators.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5e01a909ed387304fd26f804c4c78fda60d42080

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Citations in the corpus

A review on non-Hermitian skin effect (2022, background): “Some typical signatures include the localizations for an extensive number of bulk states, the breakdown of the conventional BBC and the defectiveness of the edge modes.”
Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence (2018, background): “(1) [16], which is plotted in the top row of Fig.”
Symmetry and Topology in Non-Hermitian Physics (2018, methodology): “Importantly, nonHermiticity alters the nature of the bulk-boundary correspondence [108, 116, 119, 121, 124, 130, 132–134, 136, 137, 139, 143, 144].”
Reciprocal skin effect and its realization in a topolectrical circuit (2019, background): “[18] F.”
Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class (2020, methodology): “To elucidate such a non-Bloch feature of non-Hermitian systems, recent works have developed a non-Bloch band theory that works even under arbitrary boundary conditions [25, 27, 30, 34, 40, 53, 54].”
Higher-order non-Hermitian skin effect (2020, neutral): “[47] F.”