Flat-Band Localization in Weakly Disordered System

Nishino, Seiji; Matsuda, Hiroki; Gôda, Masaki

doi:10.1143/jpsj.76.024709

Cited by 36 publications

(48 citation statements)

References 35 publications

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“…It is interesting to compare this N ln behavior to the flat band localization studied earlier [44,45]. The latter leads to a (weakly) divergent PR in the localized regime, a phenomenon that is viewed as corresponding to critical (power law type) localization.…”

Section: Pr For Type-1 Hamiltoniansmentioning

confidence: 69%

Integrals of motion for one-dimensional Anderson localized systems

et al. 2016

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Anderson localization is known to be inevitable in one-dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess 'additional' integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.

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Section: Pr For Type-1 Hamiltoniansmentioning

confidence: 69%

Integrals of motion for one-dimensional Anderson localized systems

et al. 2016

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“…Any criteria for the criticality in the spectral statistics can then be defined only locally i.e within the energy range, say δe c , in which Λ e is almost constant [20]. For example, as reported by the numerical study [2] of diamond lattice with two flat bands, the metal insulator transition occurs only at specific energies; this energy dependence of transition can theoretically be explained using Λ e (see section IV for details).…”

Section: Ensemble Complexity Parametermentioning

confidence: 99%

“…With Y − Y 0 given by eq. (9), we now have A case of two flat bands was studied in [2] for the 3-dimensional hexagonal diamond lattice. The study indicates D 2 ≈ 2.55 and 2.61 for e ∼ e k and e ∼ (e 1 + e 2 )/2, respectively.…”

Section: Transition In a Flat Band With Other Bands In The Neigh-mentioning

confidence: 99%

“…This is indeed confirmed by our results presented here which indicate existence of a critical statistics for all weak disorders and is therefore in contrast to a single critical point in the disorder driven Anderson transition. Although the disorder independence of the statistics of a weakly disordered flat band was numerically observed in previous studies [2,3,33], its critical aspects were not explored. Another feature different from the Anderson transition is the following: with increasing disorder, the spectral statistics in a flat band undergoes a Poisson → Brownian ensemble → Poisson transition, implying a localization → extended → localization transition of the eigenstates.…”

Section: Introductionmentioning

confidence: 99%

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Disorder perturbed flat bands. II. Search for criticality

Shukla

2018

Phys. Rev. B

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We present a common mathematical formulation of the level statistics of a disordered tightbinding lattice, with one or many flat bands in clean limit, in which system specific details enters through a single parameter. The formulation, applicable to both single as well as many particle flat bands, indicates the possibility of two different types of critical statistics: one in weak disorder regime (below a system specific disorder strength) and insensitive of the disorder-strength, another in strong disorder regime and occurs at specific critical disorder strengths. The single parametric dependence however relates the statistics in the two regimes (notwithstanding different scattering conditions therein). This also helps in revealing an underlying universality of the statistics in weakly disordered flat bands, shared by a wide-range of other complex systems irrespective of the origin of their complexity.

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“…The IPR is a useful quantity to distinguish the localized state from the extended state [51,[56][57][58]. The IPR is defined as p = i |φ(r i )| 4 .…”

Section: Appendix: Inverse Participation Ratiomentioning

confidence: 99%

Phase diagram of a disordered higher-order topological insulator: A machine learning study

2019

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A higher-order topological insulator is a new concept of topological states of matter, which is characterized by the emergent boundary states whose dimensionality is lower by more than two compared with that of the bulk, and draws a considerable interest. Yet, its robustness against disorders is still unclear. In this work, we investigate a phase diagram of higher-order topological insulator phases in a breathing kagome model in the presence of disorders, by using a state-of-the-art machine learning technique. We find that the corner states survive against the finite strength of disorder potential as long as the energy gap is not closed, indicating the stability of the higher-order topological phases against the disorders. arXiv:1809.09865v2 [cond-mat.dis-nn]

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Flat-Band Localization in Weakly Disordered System

Cited by 36 publications

References 35 publications

Integrals of motion for one-dimensional Anderson localized systems

Integrals of motion for one-dimensional Anderson localized systems

Disorder perturbed flat bands. II. Search for criticality

Phase diagram of a disordered higher-order topological insulator: A machine learning study

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