Proposed signature of Anderson localization and correlation-induced delocalization in an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-leg optical lattice

Sedrakyan, Tigran; Kestner, J. P.; Sarma, S. Das

doi:10.1103/physreva.84.053621

Cited by 19 publications

(15 citation statements)

References 42 publications

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“…Since this correlation has been disregarded in all previous numerical studies of the TAI which we are aware of 16,17,22,27,28 the question was posed 28 how a finite correlation length ξ would influence the predictions for the appearance and for the stability of the TAI. In view of the fact that spatial correlations in the disorder have already been shown to play an important role in the context of various other scattering scenarios [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] one may expect such correlations to be a relevant factor also for topological insulators. We address this topic by studying explicitly how a static and spatially correlated disorder influences the transport characteristics of topological insulators (Fig 1).…”

Section: Introductionmentioning

confidence: 99%

Topological insulator in the presence of spatially correlated disorder

2013

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We investigate the effect of spatially correlated disorder on two-dimensional topological insulators and on the quantum spin Hall effect which the helical edge states in these systems give rise to. Our work expands the scope of previous investigations which found that uncorrelated disorder can induce a nontrivial phase called the topological Anderson insulator (TAI). In extension of these studies, we find that spatial correlations in the disorder can entirely suppress the emergence of the TAI phase. We show that this phenomenon is associated with a quantum percolation transition and quantify it by generalizing an existing effective medium theory to the case of correlated disorder potentials. The predictions of this theory are in good agreement with our numerics and may be crucial for future experiments.

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Section: Introductionmentioning

confidence: 99%

Topological insulator in the presence of spatially correlated disorder

2013

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“…On another front, it is well-known that Anderson localization can be avoided under certain conditions for disorder potential supporting long-range [88][89][90] or shortrange [91][92][93][94][95][96][97] correlations in low dimensions. It is thus very interesting to investigate the effect of introducing correlations to the disordered interaction constant, J ijkl .…”

Section: Discussionmentioning

confidence: 99%

Supersymmetry method for interacting chaotic and disordered systems: the SYK model

Sedrakyan,

Efetov

2020

Preprint

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The nonlinear supermatrix σ-model is widely used to understand the physics of Anderson localization and the level statistics in noninteracting disordered electron systems. Here we develop a supersymmetry approach to the disorder averaging in the interacting models. In particular, we apply supersymmetry to study the Sachdev-Ye-Kitaev (SYK) model, where the disorder averaging has so far been performed only within the replica approach. We use a slightly modified, time-reversal invariant, version of the SYK model and perform calculations in real-time. As a demonstration of how the supersymmetry method works, we derive saddle point equations. In the semiclassical limit, we show that the results are in agreement with those found using the replica technique. We also develop the formally exact superbosonized representation of the SYK model. In the latter, the supersymmetric theory of original fermions and their superpartner bosons is reformulated as a model of unconstrained collective excitations. We argue that the superbosonized description of the model paves the way for the precise calculation of the window of universality in which random matrix theory is applicable to the chaotic SYK system, and for the derivation of the corresponding Wigner-Dyson eigenvalue statistics.

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“…These potentials, called short-range correlated potentials, may introduce resonance energies in the spectrum inducing delocalization of a significant subset of the eigenstates. This happens for instance in the random-dimer model (RDM) and in its dual counterpart (DRDM) [14][15][16][17], in which the sites of a lattice are assigned energies ε a or ε b at random, with the additional constraint that sites of energy ε b always appear in pairs (RDM) or never appear as neighbors (DRDM). The second class of correlated potentials is marked by a spectral function S(k) that is non-zero in a finite k-range.…”

Section: Introductionmentioning

confidence: 99%

Metal-insulator transition induced by random dipoles

et al. 2013

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Cataloged from PDF version of article.We study the localization properties of a test dipole feeling the disordered potential induced by dipolar impurities trapped at random positions in an optical lattice. This random potential is marked by correlations which are a convolution of short-range and long-range ones. We show that when short-range correlations are dominant, extended states can appear in the spectrum. Introducing long-range correlations, the extended states, if any, are wiped out and localization is restored over the whole spectrum. Moreover, long-range correlations can either increase or decrease the localization length at the center of the band, which indicates a richer behavior than previously predicted

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Proposed signature of Anderson localization and correlation-induced delocalization in anN-leg optical lattice

Cited by 19 publications

References 42 publications

Topological insulator in the presence of spatially correlated disorder

Topological insulator in the presence of spatially correlated disorder

Supersymmetry method for interacting chaotic and disordered systems: the SYK model

Metal-insulator transition induced by random dipoles

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