Multifractal finite-size scaling and universality at the Anderson transition

Rodríguez, Alejandra; Vasquez, Louella; Slevin, Keith; Römer, Rudolf A.

doi:10.1103/physrevb.84.134209

Cited by 163 publications

(273 citation statements)

References 66 publications

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“…It has been conjectured that κ c = 1 − D 1 /3, where the "information dimension" D 1 gives the amount of entropy of the critical eigenstates [28]. For the Anderson model, D 1 = 1.958 ± 0.005 [29], which leads to the prediction Λ c = κ c = 0.347, in excellent agreement with the numerically measured value Λ c = 0.342 ± 0.01. The alternate conjecture [30] 2κ c = 1 − D 2 /3 predicts κ c ≈ 0.29, deviating significantly from our numerical results.…”

Section: Figsupporting

confidence: 75%

Coherent forward scattering as a signature of Anderson metal-insulator transitions

2017

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We show that the coherent forward scattering (CFS) interference peak amplitude sharply jumps from zero to a finite value upon crossing a metal-insulator transition. Extensive numerical simulations reveal that the CFS peak contrast obeys the one-parameter scaling hypothesis and gives access to the critical exponents of the transition. We also discover that the critical CFS peak directly controls the spectral compressibility at the transition where eigenfunctions are multifractal, and we demonstrate the universality of this property with respect to various types of disorder. Related to Anderson localization (AL), coherent forward scattering (CFS) is a robust interference effect which triggers a macroscopic peak in the forward direction of the momentum distribution n(k, t) obtained after an initial plane wave |k 0 has evolved through a bulk disordered system [15][16][17]. While CFS resembles the well-known coherent backscattering (CBS) effect, which is due to the pair interference of time-reversed scattering sequences and yields a peak in the backward direction [18], the two effects turn out to be fundamentally different. Indeed, the CBS peak relies on time-reversal symmetry (TRS) [19] and exists on both sides of the MIT, with no discontinuous behavior as the mobility edge is crossed [20]. In marked contrast, CFS requires Anderson localization to show up (it is absent in the metallic phase) and is present whether or not TRS is broken [21,22]. While the experimental observation of CBS in momentum space has been recently achieved with cold atoms [23], no observation of CFS has been reported so far. On the theoretical side, CFS has been studied in one ) and metallic (bottom, W = 12J) phases of the cubic 3D Anderson model (lattice constant a, tunneling rate J) when an initial plane wave |k0 is numerically propagated up to time t = 8000 /J. The energy is set to E = J and k0 = π/(3a)êx. The CFS and CBS peaks are visible at k0 and −k0 respectively. The solid curve is a cut along kx. Right: time evolution of the normalized CFS contrast Λ in the three phases.dimension and two dimensions [15,17,21], but not in three dimensions where an Anderson MIT takes place. In this article, we numerically demonstrate that the CFS

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Section: Figsupporting

confidence: 75%

Coherent forward scattering as a signature of Anderson metal-insulator transitions

2017

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“…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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“…Such a generalised multifractal analysis has been used to perform high-precision studies of the critical properties of the transition in the non-interacting case [17][18][19][20][21][22]. This formalism is also potentially applicable in the presence of interactions, and work along this line is currently being pursued [23,24].…”

Section: Multifractal Formalismmentioning

confidence: 99%

Multifractality in Fock Space of the Ground State of the Bose-Hubbard Hamiltonian

Lindinger

Rodríguez

2017

Acta Phys. Pol. A

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We present a first study of the multifractal properties of the ground state of the Bose-Hubbard Hamiltonian in Fock space. Numerical simulations of system sizes up to L = 10 at unit filling suggest that multifractality is present for all values of the bosonic interaction strength. Moreover, the analysis of the generalised fractal dimensions for different densities exposes qualitatively the superfluid to Mott insulator phase transition.

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Multifractal finite-size scaling and universality at the Anderson transition

Cited by 163 publications

References 66 publications

Coherent forward scattering as a signature of Anderson metal-insulator transitions

Coherent forward scattering as a signature of Anderson metal-insulator transitions

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

Multifractality in Fock Space of the Ground State of the Bose-Hubbard Hamiltonian

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