30 research outputs found
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
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 plays a special role. Away from
, transport properties are those of a disordered quantum wire in
the standard unitary symmetry class. At the band center , 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
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 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
Crossover from the chiral to the standard universality classes in the conductance of a quantum wire with random hopping only
The conductance of a quantum wire with off-diagonal disorder that preserves a
sublattice symmetry (the random hopping problem with chiral symmetry) is
considered. Transport at the band center is anomalous relative to the standard
problem of Anderson localization both in the diffusive and localized regimes.
In the diffusive regime, there is no weak-localization correction to the
conductance and universal conductance fluctuations are twice as large as in the
standard cases. Exponential localization occurs only for an even number of
transmission channels in which case the localization length does not depend on
whether time-reversal and spin rotation symmetry are present or not. For an odd
number of channels the conductance decays algebraically. Upon moving away from
the band center transport characteristics undergo a crossover to those of the
standard universality classes of Anderson localization. This crossover is
calculated in the diffusive regime.Comment: 22 pages, 9 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
Critical parameters for the disorder-induced metal-insulator transition in fcc and bcc lattices
We use a transfer-matrix method to study the disorder-induced metal-insulator transition. We take isotropic nearest-neighbor hopping and an onsite potential with uniformly distributed disorder. Following the previous work done on the simple-cubic lattice, we perform numerical calculations for the body-centered cubic and face-centered cubic lattices, which are more common in nature. We obtain the localization length from calculated Lyapunov exponents for different system sizes. This data is analyzed using finite-size scaling to find the critical parameters. We create an energy-disorder phase diagram for both lattice types, noting that it is symmetric about the band center for the body-centered cubic lattice but not for the face-centered cubic lattice. We find a critical exponent of approximately 1.5-1.6 for both lattice types for transitions occurring either at fixed energy or at fixed disorder, agreeing with results previously obtained for other systems belonging to the same orthogonal universality class. We notice an increase in critical disorder with the number of nearest neighbors, which agrees with intuition