Off-Diagonal Disorder in the Anderson Model of Localization

Biswas, Parthapratim; Cain, Philipp; Röemer, Rudolf A.; Schreiber, M.

doi:10.1002/(sici)1521-3951(200003)218:1<205::aid-pssb205>3.3.co;2-2

Cited by 15 publications

(27 citation statements)

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“…Taking into account irrelevant scaling terms, we find that ν = 1.59 ± 0.05. Thus the results are again in agreement with the usual 3D case and the scaling hypothesis [114,113].…”

Section: The Anderson Model With Random Hoppingsupporting

confidence: 88%

Numerical Investigations of Scaling at the Anderson Transition

Röemer

Schreiber

2003

Anderson Localization and Its Ramifications

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“…Taking into account irrelevant scaling terms, we find that ν = 1.59 ± 0.05. Thus the results are again in agreement with the usual 3D case and the scaling hypothesis [114,113].…”

Section: The Anderson Model With Random Hoppingsupporting

confidence: 88%

Numerical Investigations of Scaling at the Anderson Transition

Röemer

Schreiber

2003

Anderson Localization and Its Ramifications

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“…This present formalism can also be extended to study off-diagonal disorder in delocalization/localization processes in low dimensions. [50][51][52] As explained in the previous sections, when system becomes localized, the PDFs of the density of states change from Gaussian distribution (where all states are metallic, the PDF is symmetric with the shape of TDOS the same as the ADOS) to a very asymmetric distribution with long tails (where all states are localized, the LDOS strongly fluctuating at all sites, and the TDOS is very different from the ADOS). Utilizing large-scale exact diagonalization calculations, Schubert et al 7 have demonstrated that the PDFs close to the Anderson transition in 2D and 3D systems are log-normal.…”

Section: Resultsmentioning

confidence: 84%

Effective cluster typical medium theory for the diagonal Anderson disorder model in one- and two-dimensions

Ekuma¹,

Terletska²,

Meng³

et al. 2014

J. Phys.: Condens. Matter

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We develop a cluster typical medium theory to study localization in disordered electronic systems. Our formalism is able to incorporate non-local correlations beyond the local typical medium theory in a systematic way. The cluster typical medium theory utilizes the momentum-resolved typical density of states and hybridization function to characterize the localization transition. We apply the formalism to the Anderson model of localization in one- and two-dimensions. In one-dimension, we find that the critical disorder strength scales inversely with the linear cluster size with a power law, Wc ∼ (1/Lc)(1/ν), whereas in two-dimensions, the critical disorder strength decreases logarithmically with the linear cluster size. Our results are consistent with previous numerical work and are in agreement with the one-parameter scaling theory.

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“…30 found Wigner-Dyson statistics in the bulk spectrum of a threedimensional chiral orthogonal disordered model. Moreover, even the critical exponent of the orthogonal and of the chiral orthogonal class turn out to be the same, up to very high numerical precision 31 . We expect the same to be true for the multifractal exponents.…”

Section: Properties Of the Dirac Operator And Details Of The Simulationsmentioning

confidence: 92%

Anderson transition and multifractals in the spectrum of the Dirac operator of quantum chromodynamics at high temperature

et al. 2015

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We investigate the Anderson transition found in the spectrum of the Dirac operator of Quantum Chromodynamics (QCD) at high temperature, studying the properties of the critical quark eigenfunctions. Applying multifractal finite-size scaling we determine the critical point and the critical exponent of the transition, finding agreement with previous results, and with available results for the unitary Anderson model. We estimate several multifractal exponents, finding also in this case agreement with a recent determination for the unitary Anderson model. Our results confirm the presence of a true Anderson localization-delocalization transition in the spectrum of the quark Dirac operator at high-temperature, and further support that it belongs to the 3D unitary Anderson model class.

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Off-Diagonal Disorder in the Anderson Model of Localization

Cited by 15 publications

References 0 publications

Numerical Investigations of Scaling at the Anderson Transition

Numerical Investigations of Scaling at the Anderson Transition

Effective cluster typical medium theory for the diagonal Anderson disorder model in one- and two-dimensions

Anderson transition and multifractals in the spectrum of the Dirac operator of quantum chromodynamics at high temperature

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