Study of localization in Anderson's model for random lattices

Licciardello, D.C.; Economou, E. N.

doi:10.1103/physrevb.11.3697

Cited by 143 publications

(40 citation statements)

References 44 publications

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“…Randomness is usually introduced by assuming that the site energies {&<} are random variables having a common probability distribution of width W taken as a measure of the degree of disorder, and the hopping matrix elements Vij are chosen t o be constant for nearest neighbors, say V , and zero otherwise. While over the last few years the effects of the above so-called diagonal disorder on the eigenstates have been studied extensively [2], very little is known on the role of the off-diagonal disorder, i.e. randomness in Vij.…”

Section: Introductionmentioning

confidence: 99%

Localization in Random Systems I. Effect of Off‐Diagonal Disorder

Brezini

Sebbani

Dahmani

1986

Physica Status Solidi (b)

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The question of localization is examined in a tight-binding Hamiltonian. The present method is based on a self-consistent theory reproducing correctly the band edge in the limit of zero disorder. Randomness is introduced also in the off-diagonal elements. In a purely diagonal disorder it is found that the results for the critical disorder W , for which the Anderson transition appears are in good agreement with other theories while for a purely off-diagonal disorder the states around the middle of the band remain extended.Die Frage der Lokalisierung wird mit einem ,,tight-binding"-Hamilton-Operator untersucht. Die Methode beruht auf einer selbstkonsistenten Theorie, welche die Bandkante im Grenzfall verschwindender Unordnung reproduziert. Die Unordnung wird auch in den nichtdiagonalen Elementen eingefuhrt. Fur eine rein diagonale Unordnung zeigen die Ergebnisse fur die kritische Unordnung W,, fur welche der Anderson-tfbergang auftritt, gute Ubereinstimmung mit anderen Theorien, wahrend fur nichtdiagonale Unordnung die ZustLnde in der Mitte des Bandes ausgedehnt bleiben.

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Section: Introductionmentioning

confidence: 99%

Localization in Random Systems I. Effect of Off‐Diagonal Disorder

Brezini

Sebbani

Dahmani

1986

Physica Status Solidi (b)

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“…The return probability is given by p 0→0 (t → ∞) = n f 2 n . 58 In case of an extended eigenstate, the residue f n is proportional to the inverse number of occupied lattice sites N −1 and the return probability approaches zero in the limit of an infinite system. In contrast, for a localized state the spectrum is given by a dense distribution of poles in the allowed energy interval on the real ω-axis.…”

Section: A Detecting Anderson Localization Within Statistical Dmftmentioning

confidence: 99%

Localization of correlated fermions in optical lattices with speckle disorder

et al. 2010

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Strongly correlated fermions in three-and two-dimensional optical lattices with experimentally realistic speckle disorder are investigated. We extend and apply the statistical dynamical mean-field theory, which treats local correlations non-perturbatively, to incorporate on-site and hopping-type randomness on equal footing. Localization due to disorder is detected via the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram for experimentally realistic parameters and find a strong suppression of the correlationinduced metal insulator transition due to disorder. Our results indicate that the Anderson-Mott and the Mott insulator are not continuously connected due to the specific character of speckle disorder. Furthermore, we discuss the effect of finite temperature on the single-particle spectral function.

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“…many substitutionally disordered alloys and disordered ferromagnets) requires the inclusion of both diagonal and off-diagonal randomness. While the role of the diagonal disorder has been extensively studied over the last several decades 21 , the effect of off-diagonal disorder is not well studied, although the effect is expected to be different. It has been shown 18,22 that off-diagonal randomness can lead to the delocalization of the states near the band-center.…”

Section: Introductionmentioning

confidence: 99%

Study of off-diagonal disorder using the typical medium dynamical cluster approximation

et al. 2014

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We generalize the typical medium dynamical cluster approximation (TMDCA) and the local Blackman, Esterling, and Berk (BEB) method for systems with off-diagonal disorder. Using our extended formalism we perform a systematic study of the effects of non-local disorder-induced correlations and off-diagonal disorder on the density of states and the mobility edge of the Anderson localized states. We apply our method to the three-dimensional Anderson model with configuration dependent hopping and find fast convergence with modest cluster sizes. Our results are in good agreement with the data obtained using exact diagonalization, and the transfer matrix and kernel polynomial methods.

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Study of localization in Anderson's model for random lattices

Cited by 143 publications

References 44 publications

Localization in Random Systems I. Effect of Off‐Diagonal Disorder

Localization in Random Systems I. Effect of Off‐Diagonal Disorder

Localization of correlated fermions in optical lattices with speckle disorder

Study of off-diagonal disorder using the typical medium dynamical cluster approximation

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