Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry

Mochizuki, Kimihiro; Kim, Dakyeong; Kawakami, Norio; Obuse, Hideaki

doi:10.1103/physreva.102.062202

Cited by 21 publications

(6 citation statements)

References 83 publications

(133 reference statements)

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“…As we detail in the online supplementary material , topological invariants defined through the global Berry phase are equivalent to winding numbers [ 36 , 37 , 41 , 42 ] or generalized Zak phases [ 35 , 43 ] in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\mathcal {PT}$\end{document} -symmetry-unbroken regime. Conversely, in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\mathcal {PT}$\end{document} -symmetry-broken regime, whereas generalized winding numbers and Zak phases become ill defined due to the emergence of ε = 0 or ε = π in the spectrum, the global Berry phases remain well defined and yield topological numbers that dictate the number of topological edge states.…”

Section: Resultsmentioning

confidence: 99%

Observation of dark edge states in parity-time-symmetric quantum dynamics

Xue

Qiu

Wang

et al. 2023

National Science Review

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Topological edge states arise in non-Hermitian parity-time ($\mathcal {PT}$)-symmetric systems, and manifest themselves as bright or dark edge states, depending on the imaginary components of their eigenenergies. As the spatial probabilities of dark edge states are suppressed during the non-unitary dynamics, it is a challenge to observe them experimentally. Here we report the experimental detection of dark edge states in photonic quantum walks with spontaneously broken $\mathcal {PT}$ symmetry, thus providing a complete description of the topological phenomena therein. We experimentally confirm that the global Berry phase in $\mathcal {PT}$-symmetric quantum-walk dynamics unambiguously defines topological invariants of the system in both the $\mathcal {PT}$-symmetry-unbroken and broken regimes. Our results establish a unified framework for characterizing topology in $\mathcal {PT}$-symmetric quantum-walk dynamics, and provide a useful method to observe topological phenomena in $\mathcal {PT}$-symmetric non-Hermitian systems in general.

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Section: Resultsmentioning

confidence: 99%

Observation of dark edge states in parity-time-symmetric quantum dynamics

Xue

Qiu

Wang

et al. 2023

National Science Review

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“…This is actually related to the P T -symmetric quantum walk defined in Ref. [22,23,24] with a gain-loss operator. The simplest version of the timeevolution operator defined there is given by…”

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confidence: 94%

Delocalization of non-Hermitian Quantum Walk on Random Media in One Dimension

Hatano,

Obuse

2021

Preprint

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Delocalization transition is numerically found in a non-Hermitian extension of a discrete-time quantum walk on a one-dimensional random medium. At the transition, an eigenvector gets delocalized and at the same time the corresponding energy eigenvalue (the imaginary unit times the phase of the eigenvalue of the time-evolution operator) becomes complex. This is in accordance with a non-Hermitian extension of the random Anderson model in one dimension, called, the Hatano-Nelson model. We thereby numerically find that all eigenstates of the Hermitian quantum walk share a common localization length.

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“…These effects are unavoidable in open quantum walks [ 13 , 14 ], which is because of the non-unitary dynamics and is described in the framework of the non-Hermitian quantum mechanics [ 23 , 24 ]. Second, PT-symmetric quantum walks and related topological properties have only been studied by the bulk–boundary corres- pondence [ 25 , 26 , 27 ], while the characterization of bulk property is thus far absent, such as diffusion property and Shannon entropy. Until very recently, the connection between diffusion property and topological property have been studied for skyrmions [ 28 ], and the relation between diffusion phenomenon and bulk–edge correspondence has been discussed [ 29 ].…”

Section: Introductionmentioning

confidence: 99%

Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks

Tian

Liu

Luo

2021

Entropy

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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.

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Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry

Cited by 21 publications

References 83 publications

Observation of dark edge states in parity-time-symmetric quantum dynamics

Observation of dark edge states in parity-time-symmetric quantum dynamics

Delocalization of non-Hermitian Quantum Walk on Random Media in One Dimension

Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks

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