Bulk-edge correspondence and robustness of edge states in a non-unitary three-step quantum walk with PT symmetry

Topological phases in non-Hermitian systems have attracted great attention in recent years. It has been shown that a photonic quantum walk with effects of loss is an ideal platform to study topological phases in non-Hermitian systems with parity-time reversal symmetry (PT symmetry)[1]. In the present work, we study topological phases and the associated multiple edge states in non-unitary three-step quantum walks with PT symmetry in one dimension[2]. We show that the non-unitary quantum walk has large topological numbers and numerically confirm that multiple edge states appear as expected from the bulk-edge correspondence. We also study stability of the edge states and find extra stabilization mechanism of the edge states unique to non-unitary systems.

[1] L. Xiao, X. Zhan, Z.H. Bian, K.K. Wang, X.Zhang, X.P.Wang, J.Li, K. Mochizuki, D. Kim, N. Kawakami, W. Yi, H. Obuse, B.C. Sanders, and P. Xue, Nature Physics, 13, 1117 (2017).
[2] M. Kawasaki, K. Mochizuki, N. Kawakami, H. Obuse, arXiv:1905.11098