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Bulk-Boundary Correspondence for Non-Hermitian Hamiltonians via Green Functions

Zirnstein, Heinrich-Gregor and Refael, Gil and Rosenow, Bernd (2021) Bulk-Boundary Correspondence for Non-Hermitian Hamiltonians via Green Functions. Physical Review Letters, 126 (21). Art. No. 216407. ISSN 0031-9007. doi:10.1103/PhysRevLett.126.216407.

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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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URLURL TypeDescription Paper
Zirnstein, Heinrich-Gregor0000-0001-7055-9959
Additional Information:© 2021 American Physical Society. Received 16 July 2020; accepted 4 May 2021; published 28 May 2021. We would like to thank T. Karzig for helpful discussions. B. R. and H.-G. Z. acknowledge financial support from the German Research Foundation within the CRC 762 (project B6). B. R. acknowledges support from the Rosi and Max Varon Visiting Professorship at the Weizmann Institute of Science. We are grateful for the hospitality of the Aspen Center for Physics, funded by NSF Grant No. PHY-1607611, where part of this work was performed. G. R. is grateful for generous support from the Institute of Quantum Information and Matter, an NSF frontier center, NSF Grant No. 1839271, and The Simons Foundation.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)CRC 762
Weizmann Institute of ScienceUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Simons FoundationUNSPECIFIED
Issue or Number:21
Record Number:CaltechAUTHORS:20190426-083909000
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95010
Deposited By: Tony Diaz
Deposited On:26 Apr 2019 16:00
Last Modified:28 May 2021 15:56

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