Localization-delocalization transition in discrete-time quantum walks with long-range correlated disorder

Mendes, C.V.C.; Almeida, G. M. A.; Lyra, Marcelo L.; Moura, F. A. B. F. de

doi:10.1103/physreve.99.022117

Cited by 15 publications

(4 citation statements)

References 59 publications

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“…This happens because coin disorder can tune the bulk topological invariant, and hence also put the system to a critical point -an example is the case where the coin rotation angle is uniformly random. We note that this localization-delocalization transition has a completely different physical origin than that induced by correlated disorder 23 .…”

Section: Introductionmentioning

confidence: 73%

Topological delocalization in the completely disordered two-dimensional quantum walk

Asbóth,

Mallick

2020

Preprint

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We investigate numerically and theoretically the effect of spatial disorder on two-dimensional split-step discrete-time quantum walks with two internal "coin" states. Spatial disorder can lead to Anderson localization, inhibiting the spread of quantum walks, putting them at a disadvantage against their diffusively spreading classical counterparts. We find that spatial disorder of the most general type, i.e., position-dependent Haar random coin operators, does not lead to Anderson localization, but to a diffusive spread instead. This is a delocalization, which happens because disorder places the quantum walk to a critical point between different anomalous Floquet-Anderson insulating topological phases. We base this explanation on the relationship of this general quantum walk to a simpler case more studied in the literature, and for which disorder-induced delocalization of a topological origin has been observed. We review topological delocalization for the simpler quantum walk, using time-evolution of the wavefunctions and level spacing statistics. We apply scattering theory to two-dimensional quantum walks, and thus calculate the topological invariants of disordered quantum walks, substantiating the topological interpretation of the delocalization, and finding signatures of the delocalization in the finite-size scaling of transmission. Our results showcase how theoretical ideas and numerical tools from solid-state physics can help us understand spatially random quantum walks.

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Section: Introductionmentioning

confidence: 73%

Topological delocalization in the completely disordered two-dimensional quantum walk

Asbóth,

Mallick

2020

Preprint

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“…QWs with correlated disorder were previously studied in both discrete- [38][39][40] and continuous-time [41,42] representations. In Refs.…”

Section: Literature Reviewmentioning

confidence: 99%

Negative correlations can play a positive role in disordered quantum walks

Pires,

Queirós

2020

Preprint

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We investigate the emerging properties of quantum walks with temporal disorder engineered from a binary Markov chain with tailored correlation, C, and disorder strength, r. We show that when the disorder is weakr 1 -the introduction of negative correlation leads to a counter-intuitive higher production of spin-lattice entanglement entropy, Se, than the setting with positive correlation, that is Se(−|C|) > Se(|C|). These results show that negatively correlated disorder plays a more important role in quantum entanglement than it has been assumed in the literature.

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“…It is basically a cellular automaton [25] whose updating rules are run by a preset sequence of quantum gates. Given recent experimental advances in the field [26][27][28] as well as their wide range of applications, from quantum algorithms [29] to simulation of involved phenomena in condensed matter physics [15,[30][31][32][33][34], DTQWs make for a suitable starting point.…”

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confidence: 99%

“…, where ν is a random number uniformly distributed within [−W, W ], with W being the disorder width. As this setting can lead to Anderson localization [15,32], we ought to inquire whether rogue waves can be supported given proper initial conditions and amount of noise embedded in F (c, n).…”

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confidence: 99%

Rogue waves in discrete-time quantum walks

Buarque,

Dias,

de Moura

et al. 2022

Preprint

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Rogue waves are rapid and unpredictable events of exceptional amplitude reported in various fields, such as oceanography and optics, with much of the interest being targeted towards their physical origins and likelihood of occurrence. Here, we use the all-round framework of discrete-time quantum walks to study the onset of those events due to a random phase modulation, unveiling its long-tailed statistics, distribution profile, and dependence upon the degree of randomness. We find that those rogue waves belong the Gumbel family of extreme value distributions.

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Localization-delocalization transition in discrete-time quantum walks with long-range correlated disorder

Cited by 15 publications

References 59 publications

Topological delocalization in the completely disordered two-dimensional quantum walk

Topological delocalization in the completely disordered two-dimensional quantum walk

Negative correlations can play a positive role in disordered quantum walks

Rogue waves in discrete-time quantum walks

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