Bulk-edge correspondence and stability of multiple edge states of a PI-symmetric non-Hermitian system by using non-unitary quantum walks

Makio Kawasaki, Ken Mochizuki, Norio Kawakami, Hideaki Obuse

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Topological phases and the associated multiple edge states are studied for parity and time-reversal (PT)-symmetric non-Hermitian open quantum systems by constructing a non-unitary three-step quantum walk retaining {PT} symmetry in one dimension. We show that the non-unitary quantum walk has large topological numbers of the {Z} topological phase and numerically confirm that multiple edge states appear as expected from the bulk-edge correspondence. Therefore, the bulk-edge correspondence is valid in this case. Moreover, we study the stability of the multiple edge states against a symmetry-breaking perturbation so that the topological phase is reduced to {Z} from {Z}. In this case, we find that the number of edge states does not become one unless a pair of edge states coalesce at an exceptional point. Thereby, this is a new kind of breakdown of the bulk-edge correspondence in non-Hermitian systems. The mechanism of the prolongation of edge states against the symmetry-breaking perturbation is unique to non-Hermitian systems with multiple edge states and anti-linear symmetry. Toward experimental verifications, we propose a procedure to determine the number of multiple edge states from the time evolution of the probability distribution.

Original languageEnglish
Article number12A105
JournalProgress of Theoretical and Experimental Physics
Volume2020
Issue number12
DOIs
Publication statusPublished - 2020 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Fingerprint Dive into the research topics of 'Bulk-edge correspondence and stability of multiple edge states of a PI-symmetric non-Hermitian system by using non-unitary quantum walks'. Together they form a unique fingerprint.

Cite this