4,407 research outputs found
Optical and dc transport properties of a strongly correlated charge density wave system: exact solution in the ordered phase of the spinless Falicov-Kimball model with dynamical mean-field theory
We derive the dynamical mean-field theory equations for transport in an
ordered charge-density-wave phase on a bipartite lattice. The formalism is
applied to the spinless Falicov-Kimball model on a hypercubic lattice at half
filling. We determine the many-body density of states, the dc charge and heat
conductivities, and the optical conductivity. Vertex corrections continue to
vanish within the ordered phase, but the density of states and the transport
coefficients show anomalous behavior due to the rapid development of thermally
activated subgap states. We also examine the optical sum rule and sum rules for
the first three moments of the Green's functions within the ordered phase and
see that the total optical spectral weight in the ordered phase either
decreases or increases depending on the strength of the interactions.Comment: 14 pages, 14 figures, submitted to Phys. Rev.
Continuum limit of the Volterra model, separation of variables and non standard realizations of the Virasoro Poisson bracket
The classical Volterra model, equipped with the Faddeev-Takhtadjan Poisson
bracket provides a lattice version of the Virasoro algebra. The Volterra model
being integrable, we can express the dynamical variables in terms of the so
called separated variables. Taking the continuum limit of these formulae, we
obtain the Virasoro generators written as determinants of infinite matrices,
the elements of which are constructed with a set of points lying on an infinite
genus Riemann surface. The coordinates of these points are separated variables
for an infinite set of Poisson commuting quantities including . The
scaling limit of the eigenvector can also be calculated explicitly, so that the
associated Schroedinger equation is in fact exactly solvable.Comment: Latex, 43 pages Synchronized with the to be published versio
Nonresonant Raman and inelastic X-ray scattering in the charge-density-wave phase of the spinless Falicov-Kimball model
Nonresonant inelastic light and X-ray scattering is investigated for the
spinless Falicov-Kimball model on an infinite-dimensional hypercubic lattice
with a charge-density-wave phase at half filling. The many-body density of
states (DOS) is found for different values of the Coulomb repulsion ,
ranging from a dirty metal to a Mott insulator. At zero temperature, the charge
gap is exactly equal to ; increasing the temperature rapidly fills the gap
with subgap states. The nonresonant response function for Raman and inelastic
X-ray scattering shows peaks connected with transitions over the gap and
transitions that involve subgap states. In the case of X-ray scattering (when
both energy and momentum are transferred), the response function illustrates
features of dynamical screening (vertex corrections) in the different
(nonresonant) symmetry channels ( and ). We also derive
and verify the first moment sum rules for the (nonresonant) Raman and inelastic
X-ray response functions.Comment: 19 pages, 17 figure
Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots
In this paper we study the coupling between a quantum dot and the edge of a
non-Abelian fractional quantum Hall state. We assume the dot is small enough
that its level spacing is large compared to both the temperature and the
coupling to the spatially proximate bulk non-Abelian fractional quantum Hall
state. We focus on the physics of level degeneracy with electron number on the
dot. The physics of such a resonant level is governed by a -channel Kondo
model when the quantum Hall state is a Read-Rezayi state at filling fraction
or its particle-hole conjugate at . The
-channel Kondo model is channel symmetric even without fine tuning any
couplings in the former state; in the latter, it is generically channel
asymmetric. The two limits exhibit non-Fermi liquid and Fermi liquid
properties, respectively, and therefore may be distinguished. By exploiting the
mapping between the resonant level model and the multichannel Kondo model, we
discuss the thermodynamic and transport properties of the system. In the
special case of , our results provide a novel venue to distinguish between
the Pfaffian and anti-Pfaffian states at filling fraction . We present
numerical estimates for realizing this scenario in experiment.Comment: 18 pages, 2 figures. Clarified final discussio
Quantum phase transition of Ising-coupled Kondo impurities
We investigate a model of two Kondo impurities coupled via an Ising
interaction. Exploiting the mapping to a generalized single-impurity Anderson
model, we establish that the model has a singlet and a (pseudospin) doublet
phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a
strong-coupling analysis and renormalization group arguments, we show that at
this transition the conductance G through the system either displays a
zero-bias anomaly, G ~ |V|^{-2(\sqrt{2}-1)}, or takes a universal value, G =
e^2/(\pi\hbar) cos^2[\pi/(2\sqrt{2})], depending on the experimental setup.
Close to the Toulouse point of the individual Kondo impurities, the
strong-coupling analysis allows to obtain the location of the phase boundary
analytically. For general model parameters, we determine the phase diagram and
investigate the thermodynamics using numerical renormalization group
calculations. In the singlet phase close to the quantum phase transtion, the
entropy is quenched in two steps: first the two Ising-coupled spins form a
magnetic mini-domain which is, in a second step, screened by a Kondoesque
collective resonance in an effective solitonic Fermi sea. In addition, we
present a flow equation analysis which provides a different mapping of the
two-impurity model to a generalized single-impurity Anderson model in terms of
fully renormalized couplings, which is applicable for the whole range of model
parameters.Comment: 24 pages, 12 figs; (v2) minor changes, flow equation section extende
Coulomb Blockade Peak Spacings: Interplay of Spin and Dot-Lead Coupling
For Coulomb blockade peaks in the linear conductance of a quantum dot, we
study the correction to the spacing between the peaks due to dot-lead coupling.
This coupling can affect measurements in which Coulomb blockade phenomena are
used as a tool to probe the energy level structure of quantum dots. The
electron-electron interactions in the quantum dot are described by the constant
exchange and interaction (CEI) model while the single-particle properties are
described by random matrix theory. We find analytic expressions for both the
average and rms mesoscopic fluctuation of the correction. For a realistic value
of the exchange interaction constant J_s, the ensemble average correction to
the peak spacing is two to three times smaller than that at J_s = 0. As a
function of J_s, the average correction to the peak spacing for an even valley
decreases monotonically, nonetheless staying positive. The rms fluctuation is
of the same order as the average and weakly depends on J_s. For a small
fraction of quantum dots in the ensemble, therefore, the correction to the peak
spacing for the even valley is negative. The correction to the spacing in the
odd valleys is opposite in sign to that in the even valleys and equal in
magnitude. These results are robust with respect to the choice of the random
matrix ensemble or change in parameters such as charging energy, mean level
spacing, or temperature.Comment: RevTex, 11 pages, 9 figures. v2: Conclusions section expanded.
Accepted for publication in PR
Reduction Operators of Linear Second-Order Parabolic Equations
The reduction operators, i.e., the operators of nonclassical (conditional)
symmetry, of (1+1)-dimensional second order linear parabolic partial
differential equations and all the possible reductions of these equations to
ordinary differential ones are exhaustively described. This problem proves to
be equivalent, in some sense, to solving the initial equations. The ``no-go''
result is extended to the investigation of point transformations (admissible
transformations, equivalence transformations, Lie symmetries) and Lie
reductions of the determining equations for the nonclassical symmetries.
Transformations linearizing the determining equations are obtained in the
general case and under different additional constraints. A nontrivial example
illustrating applications of reduction operators to finding exact solutions of
equations from the class under consideration is presented. An observed
connection between reduction operators and Darboux transformations is
discussed.Comment: 31 pages, minor misprints are correcte
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