Delocalization of a non-Hermitian quantum walk on random media in one dimension

Journal Article · Wed Dec 15 04:00:00 EST 2021 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2021.168615· OSTI ID:23183162

Hatano, Naomichi ^[1]; Obuse, Hideaki ^[2]

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1. Institute of Industrial Science, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8574 (Japan)
2. 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, Journal Name: Annals of Physics Vol. 435; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENSTATES
EIGENVALUES
EIGENVECTORS
ONE-DIMENSIONAL CALCULATIONS
PHASE TRANSFORMATIONS