Enhanced transport of two interacting quantum walkers in a one-dimensional quasicrystal with power-law hopping

Domínguez-Castro, G. A.; Paredes, R.

doi:10.1103/physreva.104.033306

Cited by 10 publications

(7 citation statements)

References 66 publications

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“…Even though QWs with temporal disorder in the coin operator have been studied for a much longer time [4][5][6][7][8][9], the QWs with temporal disorder in the displacement operator exhibits an interesting phenomenology [42][43][44][46][47][48][49][50][51][52][53][54][55][56]. In some circumstances, both types of models share some similarities, for instance, the achievement of maximal asymptotic entanglement from local states [25,26,42,43].…”

Section: Literature Reviewmentioning

confidence: 99%

Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states

Naves¹,

Pires²,

Soares-Pinto³

et al. 2022

Preprint

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Quantum walks are paradigmatic models for studies spanning from fundamental properties of quantum theory to realizations of quantum algorithms. For many years, a plethora of important results based on such models appeared in literature. Recently, a quantum walk with a nonstandard step operator was proposed and named the elephant quantum walk (EQW). With proper statistical distribution for the steps, the generalized EQW (gEQW) can be programmable to exhibit a myriad of dynamical behavior ranging from diffusion and superdiffusion to ballistic and hyperballistic spreading. Such a rich phenomenology makes the gEQW a promising model. In this work we study the influence of the statistics of the step size and the delocalization of the initial states on the entanglement entropy of the coin. Our results show that the gEQW generates maximally entangled states for almost all initial coin states and coin operators considering initially localized walkers and for the delocalized ones, taking the proper limit, the same condition is guaranteed.

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Section: Literature Reviewmentioning

confidence: 99%

Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states

Naves¹,

Pires²,

Soares-Pinto³

et al. 2022

Preprint

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“…The Aubry–André model, which also predicts localization for quasicrystalline lattices in 1D from a given value of the amplitude, is characterized by an incommensurate factor that alters the otherwise perfect crystalline order. Different realizations of quasiperiodicity refer to the election of a phase

[ 20 , 21 ]. In this work, to detect localization in a robust way, we adopted a method that, on one hand, allowed us to introduce the element of randomness in the form of a small perturbation of the quasicrystalline structure, and on the other, provided the possibility of taking the average, over a number of realizations, of the physical quantities used to identify localization.…”

Section: Modelmentioning

confidence: 99%

“…For the analysis, we considered lattices with a number of sites in the interval ∼

. Similarly to the analysis of the Aubry–André model [ 20 , 21 ], localization in these lattices was tracked in a robust way by means of a statistical analysis using multiple realizations. The index participation ratio (IPR) and the Shannon entropy were the physical quantities used to characterize localization properties.…”

Section: Introductionmentioning

confidence: 99%

Localization in Two-Dimensional Quasicrystalline Lattices

González-García

Alva‐Sánchez

Paredes

2022

Entropy

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We investigate the emergence of localization in a weakly interacting Bose gas confined in quasicrystalline lattices with three different rotational symmetries: five, eight, and twelve. The analysis, performed at a mean field level and from which localization is detected, relies on the study of two observables: the inverse participation ratio (IPR) and the Shannon entropy in the coordinate space. Those physical quantities were determined from a robust statistical study for the stationary density profiles of the interacting condensate. Localization was identified for each lattice type as a function of the potential depth. Our analysis revealed a range of the potential depths for which the condensate density becomes localized, from partially at random lattice sites to fully in a single site. We found that localization in the case of five-fold rotational symmetry appears for (6ER,9ER), while it occurs in the interval (12ER,15ER) for octagonal and dodecagonal symmetries.

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“…In fact, despite its apparent simplicity, the pair localization problem already exhibits rich physics. For instance, the enhancement of the pair localization length [40][41][42][43], the interaction effect on the dimer localization [44][45][46][47][48][49][50][51], the presence or absence of mobility edges [52,53], the fractal character of the two-body spectrum [54], and exotic dynamical regimes [55], among others. Furthermore, due to the high precision and tunability achieved on several quantum simulation platforms, the observation of few-body phenomena is within the reach of current experiments [56][57][58].…”

Section: Introductionmentioning

confidence: 99%

“…The results here discussed go beyond previous findings [42,44,47], in the sense that they explore the consequences of the range of the hopping on the two-body localization transition. Moreover, are of main relevance for current studies on the quantum dynamics of bound states in optical lattices [55,[59][60][61].…”

Section: Introductionmentioning

confidence: 99%