TY - JOUR

T1 - Bulk-edge correspondence and stability of multiple edge states of a PI-symmetric non-Hermitian system by using non-unitary quantum walks

AU - Kawasaki, Makio

AU - Mochizuki, Ken

AU - Kawakami, Norio

AU - Obuse, Hideaki

N1 - Publisher Copyright:
© 2020 The Author(s) 2020.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - 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.

AB - 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.

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U2 - 10.1093/ptep/ptaa034

DO - 10.1093/ptep/ptaa034

M3 - Article

AN - SCOPUS:85097581989

VL - 2020

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 12

M1 - 12A105

ER -