Disorder-free localization in quantum walks

Danacı, Burçin; Yalçınkaya, I.; Çakmak, Barış; Karpat, Göktuǧ; Kelly, Shane P.; Subaşı, A. L.

doi:10.1103/physreva.103.022416

Cited by 12 publications

(7 citation statements)

References 63 publications

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“…Given the quantum walks with parameter t ∈ [0, 1] described in Section 2, and suppose that the system is initially at the unit vector (15) Ψ 0 := ϕ ⊗ |0 where ϕ ∈ C 2 and ϕ = 1.…”

Section: Resultsmentioning

confidence: 99%

“…, where Ψ 0 is defined in (15). The following theorem shows that the periodic local field D n slows down the quantum velocity exponentially in the period n when the transmission parameter t is sufficiently small.…”

Section: 2mentioning

confidence: 98%

“…Very recent implementations of quantum walks in the physics literature are stressing that localization-like effects for quantum walks can be observed also in disorder free regimes, e.g., [15,43,16,11,42]. For example, quasi-periodic arrays of waveguides are proposed to realize localized quantum walks in [42], and they have been demonstrated recently in a type of optical fibers with rings of cores constructed with quasi-periodic Fibonacci sequences in [43].…”

Section: Introductionmentioning

confidence: 99%

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Exponentially decaying velocity bounds of quantum walks in periodic fields

Abdul‐Rahman¹,

Stolz²

2023

Preprint

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We consider a class of discrete-time one-dimensional quantum walks, associated with CMV unitary matrices, in the presence of a local field. This class is parametrized by a transmission parameter t ∈ [0, 1]. We show that for a certain range for t, the corresponding asymptotic velocity can be made arbitrarily small by introducing a periodic local field with a sufficiently large period. In particular, we prove an upper bound for the velocity of the n-periodic quantum walk that is decaying exponentially in the period length n. Hence, localization-like effects are observed even after a long number of quantum walk steps when n is large. 14 5. A proof of Theorem 4.3 17 5.1. Some properties of the symmetric polynomial S ,m

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“…Given the quantum walks with parameter t ∈ [0, 1] described in Section 2, and suppose that the system is initially at the unit vector (15) Ψ 0 := ϕ ⊗ |0 where ϕ ∈ C 2 and ϕ = 1.…”

Section: Resultsmentioning

confidence: 99%

Section: 2mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Exponentially decaying velocity bounds of quantum walks in periodic fields

Abdul‐Rahman¹,

Stolz²

2023

Preprint

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“…In this section, we build a model leading to a more exotic long time behavior, namely subdiffusion with an exponent 0 < γ < 1/2. Subdiffusion has already been obtained for one-dimensional quantum walks: either by using a static disorder that can be changed at each time step with a certain probability [19] or by introducing an additional degree of freedom, local spins, that interact with the quantum walker [20]. Superdiffusion (1/2 < γ < 1), another kind of anomalous diffusion, has also been observed in one-dimensional QW by applying a quasi-periodic (Fibonacci) sequence of coin [17].…”

Section: Dynamical and Spatial Disorder: Subdiffusionmentioning

confidence: 99%

Robustness of Aharonov-Bohm cages in quantum walks

Perrin,

Fuchs,

Mosseri

2022

Preprint

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It was recently shown that Aharonov-Bohm (AB) cages exist for quantum walks (QW) on certain tilings -such as the diamond chain or the dice (or T3) lattice -for a proper choice of coins. In this article, we probe the robustness of these AB cages to various perturbations. When the cages are destroyed, we analyze the leakage mechanism and characterize the resulting dynamics. Quenched disorder typically breaks the cages and leads to an exponential decay of the wavefunction similar to Anderson localization. Dynamical disorder or repeated measurements destroy phase coherence and turn the QW into a classical random walk with diffusive behavior. Combining static and dynamical disorder in a specific way leads to subdiffusion with an anomalous exponent controlled by the quenched disorder distribution. Introducing interaction to a second walker can also break the cages and restore a ballistic motion for a "molecular" bound-state.

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“…However, such an interaction-induced localization persists only for a short time [26,28]. A big step toward stable disorder-free localization is to use local constraints imposed by gauge symmetry [29,30], which turns out to be an extensive number of local conserved quantities that break ergodicity [31][32][33][34][35]. Recently, lattice gauge theories have been simulated with ultracold atom systems [36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Stable interaction-induced Anderson-like localization embedded in standing waves

Zhang

et al. 2023

New J. Phys.

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We uncover the interaction-induced \emph{stable self-localization} of few bosons in finite-size disorder-free superlattices. In these nonthermalized multi-particle states, one of the particles forms a superposition of multiple standing waves, so that it provides a quasi-random potential to localize the other particles. We derive effective Hamiltonians for self-localized states and find their energy level spacings obeying the Poisson statistics. The spatial distribution of the localized particles decays exponentially, which is refered to Anderson-like localization. Surprisingly, we find that the correlated self-localization can be solely induced by interaction in the well-studied Bose-Hubbard models, which has been overlooked for a long time. We propose a dynamical scheme to detect self-localization, where long-time quantum walks of a single particle form a superposition of multiple standing waves for trapping the subsequently loaded particles. Our work provides an experimentally feasible way to realize stable Anderson-like localization in translation-invariant disorder-free few-body systems.

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Disorder-free localization in quantum walks

Cited by 12 publications

References 63 publications

Exponentially decaying velocity bounds of quantum walks in periodic fields

Exponentially decaying velocity bounds of quantum walks in periodic fields

Robustness of Aharonov-Bohm cages in quantum walks

Stable interaction-induced Anderson-like localization embedded in standing waves

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