Multifractal properties of critical eigenstates in two-dimensional systems with symplectic symmetry

The multifractal properties of electronic eigenstates at the metal-insulator transition of a two-dimensional disordered tight-binding model with spin-orbit interaction are investigated numerically. The correlation dimensions of the spectral measure $\widetilde{D}_{2}$ and of the fractal eigenstate $D_{2}$ are calculated and shown to be related by $D_{2}=2\widetilde{D}_{2}$. The exponent $\eta=0.35\pm 0.05$ describing the energy correlations of the critical eigenstates is found to satisfy the relation $\eta=2-D_{2}$.Comment: 6 pages RevTeX; 3 uuencoded, gzipped ps-figures to appear in J. Phys. Condensed Matte

Pms2 suppresses large expansions of the (GAA·TTC)n sequence in neuronal tissues

Copyright @ 2012 Bourn et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Expanded trinucleotide repeat sequences are the cause of several inherited neurodegenerative diseases. Disease pathogenesis is correlated with several features of somatic instability of these sequences, including further large expansions in postmitotic tissues. The presence of somatic expansions in postmitotic tissues is consistent with DNA repair being a major determinant of somatic instability. Indeed, proteins in the mismatch repair (MMR) pathway are required for instability of the expanded (CAG·CTG)(n) sequence, likely via recognition of intrastrand hairpins by MutSβ. It is not clear if or how MMR would affect instability of disease-causing expanded trinucleotide repeat sequences that adopt secondary structures other than hairpins, such as the triplex/R-loop forming (GAA·TTC)(n) sequence that causes Friedreich ataxia. We analyzed somatic instability in transgenic mice that carry an expanded (GAA·TTC)(n) sequence in the context of the human FXN locus and lack the individual MMR proteins Msh2, Msh6 or Pms2. The absence of Msh2 or Msh6 resulted in a dramatic reduction in somatic mutations, indicating that mammalian MMR promotes instability of the (GAA·TTC)(n) sequence via MutSα. The absence of Pms2 resulted in increased accumulation of large expansions in the nervous system (cerebellum, cerebrum, and dorsal root ganglia) but not in non-neuronal tissues (heart and kidney), without affecting the prevalence of contractions. Pms2 suppressed large expansions specifically in tissues showing MutSα-dependent somatic instability, suggesting that they may act on the same lesion or structure associated with the expanded (GAA·TTC)(n) sequence. We conclude that Pms2 specifically suppresses large expansions of a pathogenic trinucleotide repeat sequence in neuronal tissues, possibly acting independently of the canonical MMR pathway.IDB was supported by a postdoctoral fellowship from the National Ataxia Foundation. RMP was supported by Ataxia UK. SA was supported by The Wellcome Trust. This research was made possible by grants from the National Institutes of Health (NIH/NINDS) and the Muscular Dystrophy Association to S.I.B

Universal Multifractality in Quantum Hall Systems with Long-Range Disorder Potential

We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wavefunctions at the transition energy are obtained within the framework of the generalized Chalker--Coddington network model. We determine the critical exponent $\alpha_0$ characterizing the scaling behavior of the local order parameter for systems with potential correlation length $d$ up to $12$ magnetic lengths $l$. Our results show that $\alpha_0$ does not depend on the ratio $d/l$. With increasing $d/l$, effects due to classical percolation only cause an increase of the microscopic length scale, whereas the critical behavior on larger scales remains unchanged. This proves that systems with long-range disorder belong to the same universality class as those with short-range disorder.Comment: 4 pages, 2 figures, postsript, uuencoded, gz-compresse

Multifractality of the quantum Hall wave functions in higher Landau levels

To probe the universality class of the quantum Hall system at the metal-insulator critical point, the multifractality of the wave function $\psi$ is studied for higher Landau levels, $N=1,2$, for various range $(\sigma )$ of random potential. We have found that, while the multifractal spectrum $f(\alpha)$ (and consequently the fractal dimension) does vary with $N$, the parabolic form for $f(\alpha)$ indicative of a log-normal distribution of $\psi$ persists in higher Landau levels. If we relate the multifractality with the scaling of localization via the conformal theory, an asymptotic recovery of the single-parameter scaling with increasing $\sigma$ is seen, in agreement with Huckestein's irrelevant scaling field argument.Comment: 10 pages, revtex, 5 figures available on request from [email protected]

Interactions, Localization, and the Integer Quantum Hall Effect

We report on numerical studies of the influence of Coulomb interactions on localization of electronic wavefunctions in a strong magnetic field. Interactions are treated in the Hartree-Fock approximation. Localization properties are studied both by evaluating participation ratios of Hartree-Fock eigenfunctions and by studying the boundary-condition dependence of Hartree-Fock eigenvalues. We find that localization properties are independent of interactions. Typical energy level spacings near the Fermi level and the sensitivity of those energy levels to boundary condition show similar large enhancements so that the Thouless numbers of the Hartree-Fock eigenvalues are similar to those of non-interacting electrons.Comment: 10 pages, latex (revtex 3.0), 3 figures are avaiable from S.R. Eric Yang (e-mail [email protected]

THE ANOMALOUS DIFFUSION IN HIGH MAGNETIC FIELD AND THE QUASIPARTICLE DENSITY OF STATES

We consider a disordered two-dimensional electronic system in the limit of high magnetic field at the metal-insulator transition. Density of states close to the Fermi level acquires a divergent correction to the lowest order in electron-electron interaction and shows a new power-law dependence on the energy, with the power given by the anomalous diffusion exponent $\eta$. This should be observable in the tunneling experiment with double-well GaAs heterostructure of the mobility $\propto 10^{4}V/s$ at temperatures of $\propto 10 mK$ and voltages of $\propto 1 \mu V$.Comment: 12 pages, LATEX, one figure available at request, accepted for publication in Phys. Rev.

Disordered Electrons in a Strong Magnetic Field: Transfer Matrix Approaches to the Statistics of the Local Density of States

We present two novel approaches to establish the local density of states as an order parameter field for the Anderson transition problem. We first demonstrate for 2D quantum Hall systems the validity of conformal scaling relations which are characteristic of order parameter fields. Second we show the equivalence between the critical statistics of eigenvectors of the Hamiltonian and of the transfer matrix, respectively. Based on this equivalence we obtain the order parameter exponent $\alpha_0\approx 3.4$ for 3D quantum Hall systems.Comment: 4 pages, 3 Postscript figures, corrected scale in Fig.

Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect

The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent $\eta$ and the spectral compressibility $\chi$ at the mobility edge, $\chi=\eta/2d$, is confirmed for the integer quantum Hall delocalization transition. Our calculations are performed within the framework of an unitary network-model and represent a new method to investigate spectral properties of disordered systems.Comment: 5 pages, RevTeX, 3 figures, Postscript, strongly revised version to be published in PR

Metal-insulator transitions in anisotropic 2d systems

Several phenomena related to the critical behaviour of non-interacting electrons in a disordered 2d tight-binding system with a magnetic field are studied. Localization lengths, critical exponents and density of states are computed using transfer matrix techniques. Scaling functions of isotropic systems are recovered once the dimension of the system in each direction is chosen proportional to the localization length. It is also found that the critical point is independent of the propagation direction, and that the critical exponents for the localization length for both propagating directions are equal to that of the isotropic system (approximately 7/3). We also calculate the critical value of the scaling function for both the isotropic and the anisotropic system. It is found that the isotropic value equals the geometric mean of the two anisotropic values. Detailed numerical studies of the density of states for the isotropic system reveals that for an appreciable amount of disorder the critical energy is off the band center.Comment: 6 pages RevTeX, 6 figures included, submitted to Physical Review

Quasi-localized states in disordered metals and non-analyticity of the level curvature distribution function

It is shown that the quasi-localized states in weakly disordered systems can lead to the non-analytical distribution of level curvatures. In 2D systems the distribution function P(K) has a branching point at K=0. In quasi-1D systems the non-analyticity at K=0 is very weak, and in 3D metals it is absent at all. Such a behavior confirms the conjecture that the branching at K=0 is due to the multi-fractality of wave functions and thus is a generic feature of all critical eigenstates. The relationsip between the branching power and the multi-fractality exponent $\eta(2)$ is derived.Comment: 4 pages, LATE