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Bulk-boundary correspondence for non-Hermitian Hamiltonians via Green functions

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arxiv 1901.11241 v2 pith:FWYO54MM submitted 2019-01-31 cond-mat.mes-hall physics.opticsquant-ph

Heinrich-Gregor Zirnstein , Gil Refael , Bernd Rosenow This is my paper · ORCID
classification cond-mat.mes-hallphysics.opticsquant-ph
keywords boundaryconditionsgreennon-hermitianopentopologicalbulkcorrespondence
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Genuinely non-Hermitian topological phases can be realized in open systems with sufficiently strong gain and loss; in such phases, the Hamiltonian cannot be deformed into a gapped Hermitian Hamiltonian without energy bands touching each other. Comparing Green functions for periodic and open boundary conditions we find that, in general, there is no correspondence between topological invariants computed for periodic boundary conditions, and boundary eigenstates observed for open boundary conditions. Instead, we find that the non-Hermitian winding number in one dimension signals a topological phase transition in the bulk: It implies spatial growth of the bulk Green function.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Generalized bulk-edge correspondence for non-hermitian topological systems

    cond-mat.mes-hall 2019-08 conditional novelty 6.0 of 10

    A modified periodic boundary condition with a decay parameter b makes the bulk-edge correspondence work for a non-Hermitian SSH model in an enlarged parameter space.

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

    quant-ph 2019-08 conditional novelty 6.0 of 10

    Bulk wave-packet dynamics, through the drift-velocity dependence of the Lyapunov exponent, can reveal the non-Hermitian skin effect and non-Bloch symmetry-breaking transitions.

  3. Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems

    cond-mat.str-el 2019-08 conditional novelty 6.0 of 10

    The topology of certain one-dimensional non-Hermitian chains is captured by a Chern number of an effective two-dimensional Hermitian Hamiltonian, and this hidden Chern number predicts zero-real-energy end states.

  4. Perspective on topological states of non-Hermitian lattices

    cond-mat.mes-hall 2019-09 conditional novelty 3.0 of 10

    A perspective review that attributes defectiveness in non-Hermitian lattices to boundary conditions of a hypothetical Hermitian parent system.

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