944 research outputs found
Statistical properties of eigenvectors in non-Hermitian Gaussian random matrix ensembles
Statistical properties of eigenvectors in non-Hermitian random matrix
ensembles are discussed, with an emphasis on correlations between left and
right eigenvectors. Two approaches are described. One is an exact calculation
for Ginibre's ensemble, in which each matrix element is an independent,
identically distributed Gaussian complex random variable. The other is a
simpler calculation using as an expansion parameter, where is the
rank of the random matrix: this is applied to Girko's ensemble. Consequences of
eigenvector correlations which may be of physical importance in applications
are also discussed. It is shown that eigenvalues are much more sensitive to
perturbations than in the corresponding Hermitian random matrix ensembles. It
is also shown that, in problems with time-evolution governed by a non-
Hermitian random matrix, transients are controlled by eigenvector correlations
Caustic formation in expanding condensates of cold atoms
We study the evolution of density in an expanding Bose-Einstein condensate
that initially has a spatially varying phase, concentrating on behaviour when
these phase variations are large. In this regime large density fluctuations
develop during expansion. Maxima have a characteristic density that diverges
with the amplitude of phase variations and their formation is analogous to that
of caustics in geometrical optics. We analyse in detail caustic formation in a
quasi-one dimensional condensate, which before expansion is subject to a
periodic or random optical potential, and we discuss the equivalent problem for
a quasi-two dimensional system. We also examine the influence of many-body
correlations in the initial state on caustic formation for a Bose gas expanding
from a strictly one-dimensional trap. In addition, we study a similar
arrangement for non-interacting fermions, showing that Fermi surface
discontinuities in the momentum distribution give rise in that case to sharp
peaks in the spatial derivative of the density. We discuss recent experiments
and argue that fringes reported in time of flight images by Chen and co-workers
[Phys. Rev. A 77, 033632 (2008)] are an example of caustic formation.Comment: 10 pages, 5 figures. Published versio
Critical Conductance of a Mesoscopic System: Interplay of the Spectral and Eigenfunction Correlations at the Metal-Insulator Transition
We study the system-size dependence of the averaged critical conductance
at the Anderson transition. We have: (i) related the correction to the spectral correlations; (ii) expressed
in terms of the quantum return probability; (iii) argued that
-- the critical exponent of eigenfunction correlations. Experimental
implications are discussed.Comment: minor changes, to be published in PR
Specific heat of the S=1/2 Heisenberg model on the kagome lattice: high-temperature series expansion analysis
We compute specific heat of the antiferromagnetic spin-1/2 Heisenberg model
on the kagome lattice. We use a recently introduced technique to analyze
high-temperature series expansion based on the knowledge of high-temperature
series expansions, the total entropy of the system and the low-temperature
expected behavior of the specific heat as well as the ground-state energy. In
the case of kagome-lattice antiferromagnet, this method predicts a
low-temperature peak at T/J<0.1.Comment: 6 pages, 5 color figures (.eps), Revtex 4. Change in version 3: Fig.
5 has been corrected (it now shows data for 3 different ground-state
energies). The text is unchanged. v4: corrected an error in the temperature
scale of Fig. 5. (text unchanged
Doping a topological quantum spin liquid: slow holes in the Kitaev honeycomb model
We present a controlled microscopic study of mobile holes in the spatially
anisotropic (Abelian) gapped phase of the Kitaev honeycomb model. We address
the properties of (i) a single hole [its internal degrees of freedom as well as
its hopping properties]; (ii) a pair of holes [their (relative) particle
statistics and interactions]; (iii) the collective state for a finite density
of holes. We find that each hole in the doped model has an eight-dimensional
internal space, characterized by three internal quantum numbers: the first two
"fractional" quantum numbers describe the binding to the hole of the fractional
excitations (fluxes and fermions) of the undoped model, while the third "spin"
quantum number determines the local magnetization around the hole. The
fractional quantum numbers also encode fundamentally distinct particle
properties, topologically robust against small local perturbations: some holes
are free to hop in two dimensions, while others are confined to hop in one
dimension only; distinct hole types have different particle statistics, and in
particular, some of them exhibit non-trivial (anyonic) relative statistics.
These particle properties in turn determine the physical properties of the
multi-hole ground state at finite doping, and we identify two distinct ground
states with different hole types that are stable for different model
parameters. The respective hopping dimensionalities manifest themselves in an
electrical conductivity approximately isotropic in one ground state and
extremely anisotropic in the other one. We also compare our microscopic study
with related mean-field treatments, and discuss the main discrepancies between
the two approaches, which in particular involve the possibility of binding
fractional excitations as well as the particle statistics of the holes.Comment: 29 pages, 14 figures, published version with infinitesimal change
Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class D thermal quantum Hall effect
We investigate numerically the quasiparticle density of states
for a two-dimensional, disordered superconductor in which both time-reversal
and spin-rotation symmetry are broken. As a generic single-particle description
of this class of systems (symmetry class D), we use the Cho-Fisher version of
the network model. This has three phases: a thermal insulator, a thermal metal,
and a quantized thermal Hall conductor. In the thermal metal we find a
logarithmic divergence in as , as predicted from sigma
model calculations. Finite size effects lead to superimposed oscillations, as
expected from random matrix theory. In the thermal insulator and quantized
thermal Hall conductor, we find that is finite at E=0. At the
plateau transition between these phases, decreases towards zero as
is reduced, in line with the result
derived from calculations for Dirac fermions with random mass.Comment: 8 pages, 8 figures, published versio
Strong eigenfunction correlations near the Anderson localization transition
We study overlap of two different eigenfunctions as compared with
self-overlap in the framework of an infinite-dimensional version of the
disordered tight-binding model. Despite a very sparse structure of the
eigenstates in the vicinity of Anderson transition their mutual overlap is
still found to be of the same order as self-overlap as long as energy
separation is smaller than a critical value. The latter fact explains
robustness of the Wigner-Dyson level statistics everywhere in the phase of
extended states. The same picture is expected to hold for usual d-dimensional
conductors, ensuring the form of the level repulsion at critical
point.Comment: 4 pages, RevTe
Dzyaloshinski-Moriya interactions in the kagome lattice
The kagom\'e lattice exhibits peculiar magnetic properties due to its
strongly frustated cristallographic structure, based on corner sharing
triangles. For nearest neighbour antiferromagnetic Heisenberg interactions
there is no Neel ordering at zero temperature both for quantum and classical s
pins. We show that, due to the peculiar structure, antisymmetric
Dzyaloshinsky-Moriya interactions ()
are present in this latt ice. In order to derive microscopically this
interaction we consider a set of localized d-electronic states. For classical
spins systems, we then study the phase diagram (T, D/J) through mean field
approximation and Monte-Carlo simulations and show that the antisymmetric
interaction drives this system to ordered states as soon as this interaction is
non zero. This mechanism could be involved to explain the magnetic structure of
Fe-jarosites.Comment: 4 pages, 2 figures. Presented at SCES 200
Point-Contact Conductances from Density Correlations
We formulate and prove an exact relation which expresses the moments of the
two-point conductance for an open disordered electron system in terms of
certain density correlators of the corresponding closed system. As an
application of the relation, we demonstrate that the typical two-point
conductance for the Chalker-Coddington model at criticality transforms like a
two-point function in conformal field theory.Comment: 4 pages, 2 figure
Anderson localisation in tight-binding models with flat bands
We consider the effect of weak disorder on eigenstates in a special class of
tight-binding models. Models in this class have short-range hopping on periodic
lattices; their defining feature is that the clean systems have some energy
bands that are dispersionless throughout the Brillouin zone. We show that
states derived from these flat bands are generically critical in the presence
of weak disorder, being neither Anderson localised nor spatially extended.
Further, we establish a mapping between this localisation problem and the one
of resonances in random impedance networks, which previous work has suggested
are also critical. Our conclusions are illustrated using numerical results for
a two-dimensional lattice, known as the square lattice with crossings or the
planar pyrochlore lattice.Comment: 5 pages, 3 figures, as published (this version includes minor
corrections
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