Two-Dimensional Quantum Walk with Non-Hermitian Skin Effects
Tianyu Li1, Yong-Sheng Zhang1,2*, and Wei Yi1,2*
1CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China 2CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
Abstract：We construct a two-dimensional, discrete-time quantum walk, exhibiting non-Hermitian skin effects under open-boundary conditions. As a confirmation of the non-Hermitian bulk-boundary correspondence, we show that the emergence of topological edge states is consistent with the Floquet winding number, calculated using a non-Bloch band theory, invoking time-dependent generalized Brillouin zones. Further, the non-Bloch topological invariants associated with quasienergy bands are captured by a non-Hermitian local Chern marker in real space, defined via the local biorthogonal eigenwave functions of a non-unitary Floquet operator. Our work aims to stimulate further studies of non-Hermitian Floquet topological phases where skin effects play a key role.
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2021, Vol. 38 
