Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published May 28, 2021 | Submitted + Published + Supplemental Material
Journal Article Open

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

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.

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.

Attached Files

Published - PhysRevLett.126.216407.pdf

Submitted - 1901.11241.pdf

Supplemental Material - supplement.pdf

Files

supplement.pdf
Files (2.4 MB)
Name Size Download all
md5:8594d672eaae7f0e9cbe74dc7a62694e
215.8 kB Preview Download
md5:e58a8a245bac87dc0d0690a26f73076f
1.6 MB Preview Download
md5:db5a22f1e9e47e0109a175ddec68d924
599.4 kB Preview Download

Additional details

Created:
August 20, 2023
Modified:
October 20, 2023