Finite size effects and localization properties of disordered quantum wires with chiral symmetry

Finite size effects in the localization properties of disordered quantum wires are analyzed through conductance calculations. Disorder is induced by introducing vacancies at random positions in the wire and thus preserving the chiral symmetry. For quasi one-dimensional geometries and low concentration of vacancies, an exponential decay of the mean conductance with the wire length is obtained even at the center of the energy band. For wide wires, finite size effects cause the conductance to decay following a non-pure exponential law. We propose an analytical formula for the mean conductance that reproduces accurately the numerical data for both geometries. However, when the concentration of vacancies increases above a critical value, a transition towards the suppression of the conductance occurs. This is a signature of the presence of ultra-localized states trapped in finite regions of the sample.Comment: 5 figures, revtex

Effect of Substitutional Impurities on the Electronic States and Conductivity of Crystals with Half-filled Band

Low temperature quantum corrections to the density of states (DOS) and the conductivity are examined for a two-dimensional(2D) square crystal with substitutional impurities. By summing the leading logarithmic corrections to the DOS its energy dependence near half-filling is obtained. It is shown that substitutional impurities do not suppress the van Hove singularity at the middle of the band, however they change its energy dependence strongly. Weak disorder due to substitutional impurities in the three-dimensional simple cubic lattice results in a shallow dip in the center of the band. The calculation of quantum corrections to the conductivity of a 2D lattice shows that the well-known logarithmic localization correction exists for all band fillings. Furthermore the magnitude of the correction increases as half-filling is approached. The evaluation of the obtained analytical results shows evidence for delocalized states in the center of the band of a 2D lattice with substitutional impurities

Interacting particles at a metal-insulator transition

We study the influence of many-particle interaction in a system which, in the single particle case, exhibits a metal-insulator transition induced by a finite amount of onsite pontential fluctuations. Thereby, we consider the problem of interacting particles in the one-dimensional quasiperiodic Aubry-Andre chain. We employ the density-matrix renormalization scheme to investigate the finite particle density situation. In the case of incommensurate densities, the expected transition from the single-particle analysis is reproduced. Generally speaking, interaction does not alter the incommensurate transition. For commensurate densities, we map out the entire phase diagram and find that the transition into a metallic state occurs for attractive interactions and infinite small fluctuations -- in contrast to the case of incommensurate densities. Our results for commensurate densities also show agreement with a recent analytic renormalization group approach.Comment: 8 pages, 8 figures The original paper was splitted and rewritten. This is the published version of the DMRG part of the original pape

Spectral Statistics in Chiral-Orthogonal Disordered Systems

We describe the singularities in the averaged density of states and the corresponding statistics of the energy levels in two- (2D) and three-dimensional (3D) chiral symmetric and time-reversal invariant disordered systems, realized in bipartite lattices with real off-diagonal disorder. For off-diagonal disorder of zero mean we obtain a singular density of states in 2D which becomes much less pronounced in 3D, while the level-statistics can be described by semi-Poisson distribution with mostly critical fractal states in 2D and Wigner surmise with mostly delocalized states in 3D. For logarithmic off-diagonal disorder of large strength we find indistinguishable behavior from ordinary disorder with strong localization in any dimension but in addition one-dimensional $1/|E|$ Dyson-like asymptotic spectral singularities. The off-diagonal disorder is also shown to enhance the propagation of two interacting particles similarly to systems with diagonal disorder. Although disordered models with chiral symmetry differ from non-chiral ones due to the presence of spectral singularities, both share the same qualitative localization properties except at the chiral symmetry point E=0 which is critical.Comment: 13 pages, Revtex file, 8 postscript files. It will appear in the special edition of J. Phys. A for Random Matrix Theor

Unitary limit and quantum interference effect in disordered two-dimensional crystals with nearly half-filled bands

Based on the self-consistent $T$-matrix approximation, the quantum interference (QI) effect is studied with the diagrammatic technique in weakly-disordered two-dimensional crystals with nearly half-filled bands. In addition to the usual 0-mode cooperon and diffuson, there exist $\pi$-mode cooperon and diffuson in the unitary limit due to the particle-hole symmetry. The diffusive $\pi$-modes are gapped by the deviation from the exactly-nested Fermi surface. The conductivity diagrams with the gapped $\pi$-mode cooperon or diffuson are found to give rise to unconventional features of the QI effect. Besides the inelastic scattering, the thermal fluctuation is shown to be also an important dephasing mechanism in the QI processes related with the diffusive $\pi$-modes. In the proximity of the nesting case, a power-law anti-localization effect appears due to the $\pi$-mode diffuson. For large deviation from the nested Fermi surface, this anti-localization effect is suppressed, and the conductivity remains to have the usual logarithmic weak-localization correction contributed by the 0-mode cooperon. As a result, the dc conductivity in the unitary limit becomes a non-monotonic function of the temperature or the sample size, which is quite different from the prediction of the usual weak-localization theory.Comment: 21 pages, 4 figure

Energy spectra, wavefunctions and quantum diffusion for quasiperiodic systems

We study energy spectra, eigenstates and quantum diffusion for one- and two-dimensional quasiperiodic tight-binding models. As our one-dimensional model system we choose the silver mean or `octonacci' chain. The two-dimensional labyrinth tiling, which is related to the octagonal tiling, is derived from a product of two octonacci chains. This makes it possible to treat rather large systems numerically. For the octonacci chain, one finds singular continuous energy spectra and critical eigenstates which is the typical behaviour for one-dimensional Schr"odinger operators based on substitution sequences. The energy spectra for the labyrinth tiling can, depending on the strength of the quasiperiodic modulation, be either band-like or fractal-like. However, the eigenstates are multifractal. The temporal spreading of a wavepacket is described in terms of the autocorrelation function C(t) and the mean square displacement d(t). In all cases, we observe power laws for C(t) and d(t) with exponents -delta and beta, respectively. For the octonacci chain, 0<delta<1, whereas for the labyrinth tiling a crossover is observed from delta=1 to 0<delta<1 with increasing modulation strength. Corresponding to the multifractal eigenstates, we obtain anomalous diffusion with 0<beta<1 for both systems. Moreover, we find that the behaviour of C(t) and d(t) is independent of the shape and the location of the initial wavepacket. We use our results to check several relations between the diffusion exponent beta and the fractal dimensions of energy spectra and eigenstates that were proposed in the literature.Comment: 24 pages, REVTeX, 10 PostScript figures included, major revision, new results adde

Bond-disordered Anderson model on a two dimensional square lattice - chiral symmetry and restoration of one-parameter scaling

Bond-disordered Anderson model in two dimensions on a square lattice is studied numerically near the band center by calculating density of states (DoS), multifractal properties of eigenstates and the localization length. DoS divergence at the band center is studied and compared with Gade's result [Nucl. Phys. B 398, 499 (1993)] and the powerlaw. Although Gade's form describes accurately DoS of finite size systems near the band-center, it fails to describe the calculated part of DoS of the infinite system, and a new expression is proposed. Study of the level spacing distributions reveals that the state closest to the band center and the next one have different level spacing distribution than the pairs of states away from the band center. Multifractal properties of finite systems furthermore show that scaling of eigenstates changes discontinuously near the band center. This unusual behavior suggests the existence of a new divergent length scale, whose existence is explained as the finite size manifestation of the band center critical point of the infinite system, and the critical exponent of the correlation length is calculated by a finite size scaling. Furthermore, study of scaling of Lyapunov exponents of transfer matrices of long stripes indicates that for a long stripe of any width there is an energy region around band center within which the Lyapunov exponents cannot be described by one-parameter scaling. This region, however, vanishes in the limit of the infinite square lattice when one-parameter scaling is restored, and the scaling exponent calculated, in agreement with the result of the finite size scaling analysis.Comment: 23 pages, 11 figures. RevTe

Density of States of Disordered Two-Dimensional Crystals with Half-Filled Band

A diagrammatic method is applied to study the effects of commensurability in two-dimensional disordered crystalline metals by using the particle-hole symmetry with respect to the nesting vector P_0={\pm{\pi}/a, {\pi}/a} for a half-filled electronic band. The density of electronic states (DoS) is shown to have nontrivial quantum corrections due to both nesting and elastic impurity scattering processes, as a result the van Hove singularity is preserved in the center of the band. However, the energy dependence of the DoS is strongly changed. A small offset from the middle of the band gives rise to disappearence of quantum corrections to the DoS .Comment: to be published in Physical Review Letter

The random magnetic flux problem in a quantum wire

The random magnetic flux problem on a lattice and in a quasi one-dimensional (wire) geometry is studied both analytically and numerically. The first two moments of the conductance are obtained analytically. Numerical simulations for the average and variance of the conductance agree with the theory. We find that the center of the band $\epsilon=0$ plays a special role. Away from $\epsilon=0$, transport properties are those of a disordered quantum wire in the standard unitary symmetry class. At the band center $\epsilon=0$, the dependence on the wire length of the conductance departs from the standard unitary symmetry class and is governed by a new universality class, the chiral unitary symmetry class. The most remarkable property of this new universality class is the existence of an even-odd effect in the localized regime: Exponential decay of the average conductance for an even number of channels is replaced by algebraic decay for an odd number of channels.Comment: 16 pages, RevTeX; 9 figures included; to appear in Physical Review