Level statistics and localization in a two-dimensional quantum percolation problem

Letz, M.; Ziegler, K.

doi:10.1080/13642819908206422

Cited by 7 publications

(5 citation statements)

References 23 publications

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“…The same authors [10] and earlier Meir et al [6] found evidence for a localization transition with p q < 1, based on series expansion studies. This contradicts some numerical studies [7,11,16], but agrees with other studies, which use different numerical techniques and also find a transition [14,[17][18][19][20].…”

Section: Introductioncontrasting

confidence: 53%

“…Given these limitations one should be cautious to draw conclusions on the critical behavior from series alone. There are however several other publications by independent research groups which give support to the observed behavior [11,14,[17][18][19][20][37][38][39]: • Mookerjee et al [11,40] have listed most of the above references, including the methods which were used and the conclusions. Authors using real space renormalization (RSR), recursion methods (RM), or ThoulessEdwards-Licciardello boundary perturbation methods (TEL) found transitions with p q -values ranging from 0.7 to 1 for either the site or the bond case.…”

Section: Summary Of Results and Discussionmentioning

confidence: 99%

“…For several years interest has also focused on the quantum percolation (QP) problem [4][5][6][7][8][9][10][11][12][13][14], which is a variant of the Anderson model. Here a quantum mechanical entity (single electron) propagates, as governed by Schrödinger's equation in the tight binding representation, through a lattice in which a certain fraction q = 1 − p of sites or bonds have been blocked randomly.…”

Section: Introductionmentioning

confidence: 99%

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Series expansion study of quantum percolation on the square lattice

2000

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We study the site and bond quantum percolation model on the two-dimensional square lattice using series expansion in the low concentration limit. We calculate series for the averages of P ij r k ij Tij(E), where Tij(E) is the transmission coefficient between sites i and j, for k = 0, 1, . . . , 5 and for several values of the energy E near the center of the band. In the bond case the series are of order p 14 in the concentration p (some of those have been formerly available to order p 10 ) and in the site case of order p 16 . The analysis, using the Dlog-Padé approximation and the techniques known as M1 and M2, shows clear evidence for a delocalization transition (from exponentially localized to extended or power-law-decaying states) at an energy-dependent threshold pq(E) in the range pc < pq(E) < 1, confirming previous results (e.g. pq(0.05) = 0.625 ± 0.025 and 0.740 ± 0.025 for bond and site percolation) but in contrast with the Anderson model. The divergence of the series for different k is characterized by a constant gap exponent, which is identified as the localization length exponent ν from a general scaling assumption. We obtain estimates of ν = 0.57 ± 0.10. These values violate the bound ν ≥ 2/d of Chayes et al.

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Section: Introductioncontrasting

confidence: 53%

Section: Summary Of Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Series expansion study of quantum percolation on the square lattice

2000

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“…In 2D, the situation is less clear. Here the physical community is evenly divided: one group 6,7,8,9 favors p 2D q = 1 while another group 10,11,12,13,14,15,16 claims that p 2D q < 1. The most striking argument against p 2D q < 1 comes from oneparameter scaling theory 17 , according to which arbitrary small disorder always leads to localization in 2D.…”

Section: Introductionmentioning

confidence: 99%

Dynamical aspects of two-dimensional quantum percolation

Schubert

Fehske

2008

Phys. Rev. B

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The existence of a quantum-percolation threshold p q Ͻ 1 in the two-dimensional ͑2D͒ quantum sitepercolation problem has been a controversial issue for a long time. By means of a highly efficient Chebyshev expansion technique we investigate numerically the time evolution of particle states on finite disordered square lattices with system sizes not reachable up to now. After a careful finite-size scaling, our results for the particle's recurrence probability and the distribution function of the local particle density give evidence that indeed extended states exist in the 2D percolation model for p Ͻ 1.

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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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Level statistics and localization in a two-dimensional quantum percolation problem

Cited by 7 publications

References 23 publications

Series expansion study of quantum percolation on the square lattice

Series expansion study of quantum percolation on the square lattice

Dynamical aspects of two-dimensional quantum percolation

Diffusion and localization in quantum random resistor networks

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