The Anderson Transition: Time Reversal Symmetry and Universality

Slevin, Keith; Ohtsuki, Tomi

doi:10.1103/physrevlett.78.4083

Cited by 154 publications

(214 citation statements)

References 16 publications

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“…Furthermore, in ref. [9] the correlation-length critical exponent was found to be compatible with that of the 3D unitary Anderson model [41]. Here "unitary" refers to the symmetry class of the model in the Random Matrix Theory (RMT) classification of random matrix ensembles [42], which is shared by the staggered Dirac operator [35].…”

Section: Jhep02(2017)055mentioning

confidence: 99%

Deconfinement, chiral transition and localisation in a QCD-like model

Giordano¹,

Katz²,

Kovács³

et al. 2017

J. High Energ. Phys.

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Abstract:We study the problems of deconfinement, chiral symmetry restoration and localisation of the low Dirac eigenmodes in a toy model of QCD, namely unimproved staggered fermions on lattices of temporal extension N T = 4. This model displays a genuine deconfining and chirally-restoring first-order phase transition at some critical value of the gauge coupling. Our results indicate that the onset of localisation of the lowest Dirac eigenmodes takes place at the same critical coupling where the system undergoes the first-order phase transition. This provides further evidence of the close relation between deconfinement, chiral symmetry restoration and localisation of the low modes of the Dirac operator on the lattice.

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Section: Jhep02(2017)055mentioning

confidence: 99%

Deconfinement, chiral transition and localisation in a QCD-like model

Giordano¹,

Katz²,

Kovács³

et al. 2017

J. High Energ. Phys.

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show abstract

“…Also notice that the cluster Green function (G c ) ij and its components G AA c , G BB c and G AB c are defined in the same way as in Eqs. (6)(7)(8)(9).…”

Section: B Typical Medium Theory With Off-diagonal Disordermentioning

confidence: 99%

“…Despite progress over the last decades, the subject of Anderson localization remains an active area of research. The lack of quantitative analytical results has meant that numerical investigations [5][6][7][8][9][10][11] have provided a significant role in understanding the Anderson transition 12-14 .…”

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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“…Two different numerical studies reported two different forms of P*(g) for the same system, 9,10 and it was found that the difference originates in the use of different boundary conditions ͑BC's͒. 11 The idea that P*(g) might depend on the BC's indeed appears very natural after the discovery that spectral statistics, and in particular the energy level spacing distribution P(s) exactly at the MIT, do depend on the BC's.…”

Section: Introductionmentioning

confidence: 99%

Boundary conditions, the critical conductance distribution, and one-parameter scaling

Braun¹,

Hofstetter

Montambaux

et al. 2001

Phys. Rev. B

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We study the influence of boundary conditions transverse to the transport direction for disordered mesoscopic conductors both at the Anderson metal-insulator transition and in the metallic regime. We show that the boundary conditions strongly influence the conductance distribution exactly at the metal-insulator transition and we discuss implications for the standard picture of one-parameter scaling. We show in particular that the scaling function that describes the change of conductance with system size depends on the boundary conditions from the metallic regime up to the metal-insulator transition. An experiment is proposed that might test the correctness of the one-parameter scaling theory.

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The Anderson Transition: Time Reversal Symmetry and Universality

Cited by 154 publications

References 16 publications

Deconfinement, chiral transition and localisation in a QCD-like model

Deconfinement, chiral transition and localisation in a QCD-like model

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

Boundary conditions, the critical conductance distribution, and one-parameter scaling

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