Quantum and classical localization in the lowest Landau level

Sandler, Nancy; Maei, Hamid R.; Kondev, Jané

doi:10.1103/physrevb.68.205315

Cited by 10 publications

(13 citation statements)

References 21 publications

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“…Marginally localized states show anomalous subdiffusive dynamics, as is known from previous studies of dynamics in disordered quantum Hall systems [39][40][41]. These results are reproduced by the following simple argument.…”

Section: A Subdiffusive Relaxationsupporting

confidence: 77%

Marginal Anderson localization and many-body delocalization

2014

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We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent ν. This class includes disordered systems with intrinsic-or symmetry-protectedtopological bands, such as disordered integer quantum Hall insulators. In the absence of interactions, such marginally localized systems exhibit anomalous properties intermediate between localized and extended including: vanishing DC conductivity but sub-diffusive dynamics, and fractal entanglement (an entanglement entropy with a scaling intermediate between area and volume law). We investigate the stability of marginal localization in the presence of interactions, and argue that arbitrarily weak short range interactions trigger delocalization for partially filled bands at non-zero energy density if ν ≥ 1/d. We use the Harris/Chayes bound ν ≥ 2/d, to conclude that marginal localization is generically unstable in the presence of interactions. Our results suggest the impossibility of stabilizing quantized Hall conductance at non-zero energy density.

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Section: A Subdiffusive Relaxationsupporting

confidence: 77%

Marginal Anderson localization and many-body delocalization

2014

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“…Preliminary results of our numerical approach were reported in Ref. 6. Here we provide a detailed account of the numerical methods used to study the effect of power-law correlated disorder potentials on the integer quantum Hall transition (IQHT), as well as theoretical arguments supporting them.…”

Section: Introductionmentioning

confidence: 93%

Correlated quantum percolation in the lowest Landau level

Sandler¹,

Maei²,

Kondev³

2004

Phys. Rev. B

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Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically electron localization in the lowest Landau level in the presence of a power-law correlated disorder potential. Careful comparisons between classical and quantum dynamics suggest that the extended Harris criterion is applicable in the quantum case. This leads to a prediction of new localization quantum critical points in integer quantum Hall systems with powerlaw correlated disorder potentials. We demonstrate the stability of these critical points to addition of competing short-range disorder potentials, and discuss possible experimental realizations.

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“…Current applications concern e.g. transport properties of doped semiconductors 4 and granular metals 5 , metal-insulator transition in twodimensional n-GaAs heterostructures 6 , wave propagation through binary inhomogeneous media 7 , superconductorinsulator and (integer) quantum Hall transitions 8,9 , or the dynamics of atomic Fermi-Bose mixtures 10 . Another important example is the metal-insulator transition in perovskite manganite films and the related colossal magnetoresistance effect, which in the meantime are believed to be inherently percolative.…”

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confidence: 99%

Localization effects in quantum percolation

2005

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We present a detailed study of the quantum site percolation problem on simple cubic lattices, thereby focussing on the statistics of the local density of states and the spatial structure of the single particle wavefunctions. Using the Kernel Polynomial Method we refine previous studies of the metal-insulator transition and demonstrate the non-monotonic energy dependence of the quantum percolation threshold. Remarkably, the data indicates a "fragmentation" of the spectrum into extended and localised states. In addition, the observation of a chequerboard-like structure of the wavefunctions at the band centre can be interpreted as anomalous localisation.PACS numbers: 71.23. An, 71.30.+h, 05.60.Gg, 72.15.Rn Disordered structures attracted continuing interest over the last decades, and besides the Anderson localisation problem 1 quantum percolation 2,3 is one of the classical subjects of this field. Current applications concern e.g. transport properties of doped semiconductors 4 and granular metals 5 , metal-insulator transition in twodimensional n-GaAs heterostructures 6 , wave propagation through binary inhomogeneous media 7 , superconductorinsulator and (integer) quantum Hall transitions 8,9 , or the dynamics of atomic Fermi-Bose mixtures 10 . Another important example is the metal-insulator transition in perovskite manganite films and the related colossal magnetoresistance effect, which in the meantime are believed to be inherently percolative. 11 In disordered solids the percolation problem is characterised by the interplay of pure classical and quantum effects. Besides the question of finding a percolating path of "accessible" sites through a given lattice the quantum nature of the electrons imposes further restrictions on the existence of extended states and, consequently, of a finite DC-conductivity. As a particularly simple model describing this situation we consider a tight-binding oneelectron Hamiltonian,on a simple cubic lattice with N = L 3 sites and random on-site energies ǫ i drawn from the bimodal distributionThe two energies ǫ A and ǫ B could, for instance, represent the potential landscape of a binary alloy A p B 1−p , where each site is occupied by an A or B atom with probability p or 1−p, respectively. In the limit ∆ = (ǫ B −ǫ A ) → ∞ the wavefunction of the A sub-band vanishes identically on the B-sites, making them completely inaccessible for the quantum particles. We then arrive at a situation where non-interacting electrons move on a random ensemble of lattice points, which, depending on p, may span the entire lattice or not. The corresponding Hamiltonian readswhere the summation extends over nearest-neighbour Asites only and, without loss of generality, ǫ A is chosen to be zero. Within the classical percolation scenario the percolation threshold p c is defined by the occurrence of an infinite cluster A ∞ of adjacent A sites. For the simple cubic lattice this site-percolation threshold is p c = 0.3117. 12 In the quantum case, the multiple scattering of the particles at the irregular boundari...

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Quantum and classical localization in the lowest Landau level

Cited by 10 publications

References 21 publications

Marginal Anderson localization and many-body delocalization

Marginal Anderson localization and many-body delocalization

Correlated quantum percolation in the lowest Landau level

Localization effects in quantum percolation

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