Dynamical aspects of two-dimensional quantum percolation

Schubert, G.; Fehske, Holger

doi:10.1103/physrevb.77.245130

Cited by 26 publications

(32 citation statements)

References 35 publications

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“…5 a comparison of the average and typical DOS calculated with the DCA and the TMDCA (N c = 4 3 ) as compared with the kernel polynomial method (KPM). [47][48][49][50] In the KPM analysis, instead of diagonalizing the Hamiltonian directly, the local DOS is expressed in term of an infinite series of Chebyshev polynomials. In practice, the truncated series leads to Gibbs oscillations.…”

Section: B Typical Medium Finite Cluster Analysis Of Diagonal and Ofmentioning

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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Section: B Typical Medium Finite Cluster Analysis Of Diagonal and Ofmentioning

confidence: 99%

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

et al. 2014

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“…Since in two dimensions the problem of quantum percolation is still discussed controversially-especially with respect to the existence of a quantum percolation threshold p c ≤ p q ≤ 1, see, e.g., Refs. 25,26,27,28,29,30,31,32,33,34,35,36-we rely on unbiased numerical techniques, which take quantum effects fully into account. To this end we employ the so-called local distribution (LD) approach 37,38 .…”

Section: Introductionmentioning

confidence: 99%

Diffusion and localization in quantum random resistor networks

Schubert

Fehske

2008

Phys. Rev. B

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The theoretical description of transport in a wide class of novel materials is based upon quantum percolation and related random resistor network (RRN) models. We examine the localization properties of electronic states of diverse two-dimensional quantum percolation models using exact diagonalization in combination with kernel polynomial expansion techniques. Employing the local distribution approach we determine the arithmetically and geometrically averaged densities of states in order to distinguish extended, current carrying states from localized ones. To get further insight into the nature of eigenstates of RRN models we analyze the probability distribution of the local density of states in the whole parameter and energy range. For a recently proposed RRN representation of graphene sheets we discuss leakage effects.

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“…8, we would generally expect quantum fluctuations to lead to backscattering, which may hinder conductance. References [17,40] showed, using large scale numerics with the kernel polynomial methods, that the quantum percolation threshold p q c < 1, and we necessarily have p c ≤ p q c . Furthermore, studies on the Bethe lattice seem to show that the quantum site percolation threshold agrees with the classical threshold [39], and our results are also consistent with the classical site percolation on a square lattice.…”

Section: Iid Delocalization In 2d and Quantum Percolationmentioning

confidence: 99%

“…The honeycomb Kitaev model can itself be understood in terms of itinerant Majorana fermions coupled to static Z 2 gauge fields. Other examples include the resonating valencebond liquid [8,9], slave-particle descriptions of the Hubbard model [10,11], non-Fermi metals [12] and glasses [13], the Falicov-Kimball model [14][15][16][17], etc. While models of lattice gauge theories are often difficult to realize in experiment, recent developments in cold atom quantum simulators have opened possibilities in studying these models, see, e.g., the pioneering experiment on cold ion simulations of the Schwinger model [18].…”

Section: Introductionmentioning

confidence: 99%

Dynamical localization in ℤ2 lattice gauge theories

Smith¹,

Knolle

Moessner

et al. 2018

Phys. Rev. B

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We study quantum quenches in two-dimensional lattice gauge theories with fermions coupled to dynamical Z2 gauge fields. Through the identification of an extensive set of conserved quantities, we propose a generic mechanism of charge localization in the absence of quenched disorder both in the Hamiltonian and in the initial states. We provide diagnostics of this localization through a set of experimentally relevant dynamical measures, entanglement measures, as well as spectral properties of the model. One of the defining features of the models that we study is a binary nature of emergent disorder, related to Z2 degrees of freedom. This results in a qualitatively different behaviour in the strong disorder limit compared to typically studied models of localization. For example it gives rise to a possibility of a delocalization transition via a mechanism of quantum percolation in dimensions higher than 1D. We highlight the importance of our general phenomenology to questions related to dynamics of defects in Kitaev's toric code, and to quantum quenches in Hubbard models. While the simplest models we consider are effectively non-interacting, we also include interactions leading to many-body localization-like logarithmic entanglement growth. Finally, we consider effects of interactions that generate dynamics for conserved charges, which gives rise to only transient localization behaviour, or quasi-many-bodylocalization.arXiv:1803.06574v2 [cond-mat.str-el]

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Dynamical aspects of two-dimensional quantum percolation

Cited by 26 publications

References 35 publications

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

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

Diffusion and localization in quantum random resistor networks

Dynamical localization in ℤ2 lattice gauge theories

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