2021/08/31 by Zhiyu Tian, Zhi-Yu Tian, Yang Liu +1
Computer Science · Mathematics · Physics and Astronomy · #Entropy (arrow of time) #Hermitian matrix #Mathematics #Parity (physics) #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Quantum algorithm #Quantum mechanics #Quantum phase transition #Quantum walk #Random walk #Statistical physics #Statistics #Topological Materials and Phenomena #Topological entropy in physics #Topological order #Topological quantum number #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.3390/e23091145
published as Entropy 2021, 23(9), 1145
openalex publication_date 2021/08/31 · arxiv created 2022/01/24 · arxiv updated 2022/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk-boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The diffusion coefficient was found to show unique features with the topological phase transitions driven by parity-time (PT)-symmetric non-Hermitian discrete-time quantum walks as well as by Hermitian ones, despite the fact that artificial boundaries are not constructed by an inhomogeneous quantum walk. For a Hermitian system, a turning point and abrupt change appears in the diffusion coefficient when the system is approaching the topological phase transition, while it remains stable in the trivial topological state. For a non-Hermitian system, except for the feature associated with the topological transition, the diffusion coefficient in the PT-symmetric-broken phase demonstrates an abrupt change with a peak structure. In addition, the Shannon entropy of the quantum walk is found to exhibit a direct correlation with the diffusion coefficient. The numerical results presented herein may open up a new avenue for studying the topological state in non-Hermitian quantum walk systems.