Phase diagram in the kicked Harper model

Artuso, Roberto; Borgonovi, Fausto; Guarneri, Italo; Rebuzzini, Laura; Casati, Giulio

doi:10.1103/physrevlett.69.3302

Cited by 75 publications

(72 citation statements)

References 14 publications

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“…Insights on many topics have been gained from studies of this model. Such topics include metal-insulator transitions [56][57][58] and quantum eigenstate topology 59,60 . Remarkably, the KHM displays an unusual fractal-like quasienergy spectrum due to its close connection 44 with the famous…”

Section: Two Dynamical Models and Their Implementations On A Latticementioning

confidence: 99%

Topological effects in chiral symmetric driven systems

Gong

2014

Phys. Rev. B

107

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Recent years have seen a strong interest in topological effects within periodically driven systems.In this work, we explore topological effects in two closely related 2-dimensional driven systems described by Floquet operators possessing chiral symmetry (CS). Our numerical and analytical results suggest the following. Firstly, the CS is associated with the existence of the anomalous counter-propagating (ACP) modes reported recently. Specifically, we show that a particular form of CS protects the ACP modes occurring at quasienergies of ±π. We also find that these modes are only present along selected boundaries, suggesting that they are a weak topological effect. Secondly, we find that CS can give rise to protected 0 and π quasienergy modes, and that the number of these modes may increase without bound as we tune up certain system parameters. Like the ACP modes, these 0 and π modes also appear only along selected boundaries and thus appear to be a weak topological effect. To our knowledge, this work represents the first detailed study of weak topological effects in periodically driven systems. Our findings add to the still-growing knowledge on driven topological systems.

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Section: Two Dynamical Models and Their Implementations On A Latticementioning

confidence: 99%

Topological effects in chiral symmetric driven systems

Gong

2014

Phys. Rev. B

107

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“…In this regime of partial delocalization, an initial wave packet will spread, but a certain fraction of the total probability will remain localized. In addition, the diffusion of probability in momentum space has been shown numerically to be anomalous, with an exponent depending on the parameter values [17,22,23]. These properties are summarized by the phase diagram of Fig.3.…”

Section: Harper and Kicked Harper Modelsmentioning

confidence: 97%

“…This spectrum has been the focus of many studies (see e.g. [23]): it shows multifractal properties, and transport properties (localized or delocalized states) are reflected in the eigenvalues, as well as dynamical properties (chaotic or integrable states). Additionally, for small K = L, this spectrum will be close to the famous spectrum of the Harper model ("Hofstadter butterfly"), which shows fractal properties [15], as can be seen in Fig.24.…”

Section: Spectrum: Measurement and Imperfection Effectsmentioning

confidence: 99%

“…This system has been the subject of many studies in the past few years, which focused on localization properties [20,21,22,23,24,25,26,27], tunneling properties [28,29], etc...…”

Section: Harper and Kicked Harper Modelsmentioning

confidence: 99%

“…For most of the results of this paper, the phase space will be a cylinder closed in the θ direction (Q = 1) and extended in the direction of momentum, and transport properties will be studied in the momentum direction, as in the kicked rotator. In this case /(2π) was set to 1/(6 + 1/(( √ 5 − 1)/2)) = (13 − √ 5)/82 as in [23] to avoid unwanted arithmetical effects. The choice of a constant implies that changing the number of qubits leads to increasing the size of phase space (number of cells) in the n direction.…”

Section: Harper and Kicked Harper Modelsmentioning

confidence: 99%

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Quantum computation of a complex system: The kicked Harper model

Lévi

Georgeot

2004

Phys. Rev. E

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The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting phenomena such as fractal spectra, mixed phase space, dynamical localization, anomalous diffusion, or partial delocalization, and can describe electrons in a magnetic field. Three different quantum algorithms are presented and analyzed, enabling to simulate efficiently the evolution operator of this system with different precision using different resources. Depending on the parameters chosen, the system is near-integrable, localized, or partially delocalized. In each case we identify transport or spectral quantities which can be obtained more efficiently on a quantum computer than on a classical one. In most cases, a polynomial gain compared to classical algorithms is obtained, which can be quadratic or less depending on the parameter regime. We also present the effects of static imperfections on the quantities selected, and show that depending on the regime of parameters, very different behaviors are observed. Some quantities can be obtained reliably with moderate levels of imperfection, whereas others are exponentially sensitive to imperfection strength. In particular, the imperfection threshold for delocalization becomes exponentially small in the partially delocalized regime. Our results show that interesting behavior can be observed with as little as 7-8 qubits, and can be reliably measured in presence of moderate levels of internal imperfections.

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Quantum Chaos and Spectral Transitions in the Kicked Harper Model

Kruse

Ketzmerick

Geisel

Statistical and Dynamical Aspects of Mesoscopic Systems

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Phase diagram in the kicked Harper model

Cited by 75 publications

References 14 publications

Topological effects in chiral symmetric driven systems

Topological effects in chiral symmetric driven systems

Quantum computation of a complex system: The kicked Harper model

Quantum Chaos and Spectral Transitions in the Kicked Harper Model

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