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

Zirnstein, Heinrich-Gregor and Refael, Gil and Rosenow, Bernd (2019) Bulk-boundary correspondence for non-Hermitian Hamiltonians via Green functions. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190426-083909000

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Abstract

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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1901.11241arXivDiscussion Paper
Additional Information: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 Collaborative Research Centre 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 PHY-1607611, where part of this work was performed. G. R. is grateful for support from the Institute of Quantum Information and Matter, an NSF frontier center.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
Weizmann Institute of ScienceUNSPECIFIED
NSFPHY-1607611
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Record Number:CaltechAUTHORS:20190426-083909000
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190426-083909000
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95010
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Apr 2019 16:00
Last Modified:26 Apr 2019 16:00

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