Delocalization of a non-Hermitian quantum walk on random media in one dimension
- Institute of Industrial Science, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8574 (Japan)
- Department of Applied Physics, Hokkaido University, Sapporo 060-8628 (Japan)
Highlights: • We study the localization-delocalization transition of a non-Hermitian quantum walk. • We find that the phase transition is similar to the one in the Hatano-Nelson model. • All eigenvectors get extended and all eigenvalues become complex at the transition. • This implies that the localization lengths of all eigenvectors are the same. We first review the localization–delocalization transition of a non-Hermitian random tight-binding Anderson model, called the Hatano–Nelson model. We then report a new result for a non-Hermitian extension of a discrete-time quantum walk on a one-dimensional random medium; we numerically find a delocalization transition similar to one of the Hatano–Nelson model. As a common feature to both models, at the transition point, an eigenvector gets delocalized and at the same time the corresponding energy eigenvalue (for the latter quantum-walk model, the imaginary unit times the phase of the eigenvalue of the time-evolution operator) becomes complex. One of the unique properties of the present non-Hermitian quantum walk is that the localization length of all eigenvectors is the same, and thereby all eigenstates simultaneously undergo the delocalization transition and all energy eigenvalues become complex at the same time when we turn up a non-Hermitian parameter.
- OSTI ID:
- 23183162
- Journal Information:
- Annals of Physics, Vol. 435; Other Information: Copyright (c) 2021 Elsevier Inc. All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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