484 research outputs found
Numerical renormalization group study of the symmetric Anderson-Holstein model: phonon and electron spectral functions
We study the symmetric Anderson-Holstein (AH) model at zero temperature with
Wilson's numerical renormalization group (NRG) technique to study the interplay
between the electron-electron and electron-phonon interactions. An improved
method for calculating the phonon propagator using the NRG technique is
presented, which turns out to be more accurate and reliable than the previous
works in that it calculates the phonon renormalization explicitly and satisfies
the boson sum rule better. The method is applied to calculate the renormalized
phonon propagators along with the electron propagators as the onsite Coulomb
repulsion and electron-phonon coupling constant are varied. As is
increased, the phonon mode is successively renormalized, and for crosses over to the regime where the mode splits into two components,
one of which approaches back to the bare frequency and the other develops into
a soft mode. The initial renormalization of the phonon mode, as is
increased from 0, depends on and the hybridization ; it gets
softened (hardened) for . Correlated with
the emergence of the soft mode is the central peak of the electron spectral
function severely suppressed. These NRG calculations will be compared with the
standard Green's function results for the weak coupling regime to understand
the phonon renormalization and soft mode.Comment: 18 pages, 4 figures. Submitted to Phys. Rev.
Magnetic properties of the Anderson model: a local moment approach
We develop a local moment approach to static properties of the symmetric
Anderson model in the presence of a magnetic field, focussing in particular on
the strong coupling Kondo regime. The approach is innately simple and
physically transparent; but is found to give good agreement, for essentially
all field strengths, with exact results for the Wilson ratio, impurity
magnetization, spin susceptibility and related properties.Comment: 7 pages, 3 postscript figues. Latex 2e using the epl.cls Europhysics
Letters macro packag
Field-dependent dynamics of the Anderson impurity model
Single-particle dynamics of the Anderson impurity model in the presence of a
magnetic field are considered, using a recently developed local moment
approach that encompasses all energy scales, field and interaction strengths.
For strong coupling in particular, the Kondo scaling regime is recovered. Here
the frequency () and field ()
dependence of the resultant universal scaling spectrum is obtained in large
part analytically, and the field-induced destruction of the Kondo resonance
investigated. The scaling spectrum is found to exhibit the slow logarithmic
tails recently shown to dominate the zero-field scaling spectrum. At the
opposite extreme of the Fermi level, it gives asymptotically exact agreement
with results for statics known from the Bethe ansatz. Good agreement is also
found with the frequency and field-dependence of recent numerical
renormalization group calculations. Differential conductance experiments on
quantum dots in the presence of a magnetic field are likewise considered; and
appear to be well accounted for by the theory. Some new exact results for the
problem are also established
A Local Moment Approach to magnetic impurities in gapless Fermi systems
A local moment approach is developed for the single-particle excitations of a
symmetric Anderson impurity model (AIM), with a soft-gap hybridization
vanishing at the Fermi level with a power law r > 0. Local moments are
introduced explicitly from the outset, and a two-self-energy description is
employed in which the single-particle excitations are coupled dynamically to
low-energy transverse spin fluctuations. The resultant theory is applicable on
all energy scales, and captures both the spin-fluctuation regime of strong
coupling (large-U), as well as the weak coupling regime. While the primary
emphasis is on single particle dynamics, the quantum phase transition between
strong coupling (SC) and (LM) phases can also be addressed directly; for the
spin-fluctuation regime in particular a number of asymptotically exact results
are thereby obtained. Results for both single-particle spectra and SC/LM phase
boundaries are found to agree well with recent numerical renormalization group
(NRG) studies. A number of further testable predictions are made; in
particular, for r < 1/2, spectra characteristic of the SC state are predicted
to exhibit an r-dependent universal scaling form as the SC/LM phase boundary is
approached and the Kondo scale vanishes. Results for the `normal' r = 0 AIM are
moreover recovered smoothly from the limit r -> 0, where the resultant
description of single-particle dynamics includes recovery of Doniach-Sunjic
tails in the Kondo resonance, as well as characteristic low-energy Fermi liquid
behaviour.Comment: 52 pages, 19 figures, submitted to Journal of Physics: Condensed
Matte
Bound states in straight quantum waveguides with combined boundary conditions
We investigate the discrete spectrum of the Hamiltonian describing a quantum
particle living in the two-dimensional straight strip. We impose the combined
Dirichlet and Neumann boundary conditions on different parts of the boundary.
Several statements on the existence or the absence of the discrete spectrum are
proven for two models with combined boundary conditions. Examples of
eigenfunctions and eigenvalues are computed numerically.Comment: 24 pages, LaTeX 2e with 4 eps figure
Finite temperature numerical renormalization group study of the Mott-transition
Wilson's numerical renormalization group (NRG) method for the calculation of
dynamic properties of impurity models is generalized to investigate the
effective impurity model of the dynamical mean field theory at finite
temperatures. We calculate the spectral function and self-energy for the
Hubbard model on a Bethe lattice with infinite coordination number directly on
the real frequency axis and investigate the phase diagram for the Mott-Hubbard
metal-insulator transition. While for T<T_c approx 0.02W (W: bandwidth) we find
hysteresis with first-order transitions both at U_c1 (defining the insulator to
metal transition) and at U_c2 (defining the metal to insulator transition), at
T>T_c there is a smooth crossover from metallic-like to insulating-like
solutions.Comment: 10 pages, 9 eps-figure
Mott-Hubbard Transition and Anderson Localization: Generalized Dynamical Mean-Field Theory Approach
Density of states, dynamic (optical) conductivity and phase diagram of
strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model
are analyzed within the generalized dynamical mean field theory (DMFT+\Sigma
approximation). Strong correlations are accounted by DMFT, while disorder is
taken into account via the appropriate generalization of self-consistent theory
of localization. The DMFT effective single impurity problem is solved by
numerical renormalization group (NRG) and we consider the three-dimensional
system with semi-elliptic density of states. Correlated metal, Mott insulator
and correlated Anderson insulator phases are identified via the evolution of
density of states and dynamic conductivity, demonstrating both Mott-Hubbard and
Anderson metal-insulator transition and allowing the construction of complete
zero-temperature phase diagram of Anderson-Hubbard model. Rather unusual is the
possibility of disorder induced Mott insulator to metal transition.Comment: 15 pages, 16 figure
Single-particle dynamics of the Anderson model: a local moment approach
A non-perturbative local moment approach to single-particle dynamics of the
general asymmetric Anderson impurity model is developed. The approach
encompasses all energy scales and interaction strengths. It captures thereby
strong coupling Kondo behaviour, including the resultant universal scaling
behaviour of the single-particle spectrum; as well as the mixed valent and
essentially perturbative empty orbital regimes. The underlying approach is
physically transparent and innately simple, and as such is capable of practical
extension to lattice-based models within the framework of dynamical mean-field
theory.Comment: 26 pages, 9 figure
Multichannel pseudogap Kondo model: Large-N solution and quantum-critical dynamics
We discuss a multichannel SU(N) Kondo model which displays non-trivial
zero-temperature phase transitions due to a conduction electron density of
states vanishing with a power law at the Fermi level. In a particular large-N
limit, the system is described by coupled integral equations corresponding to a
dynamic saddle point. We exactly determine the universal low-energy behavior of
spectral densities at the scale-invariant fixed points, obtain anomalous
exponents, and compute scaling functions describing the crossover near the
quantum-critical points. We argue that our findings are relevant to recent
experiments on impurity-doped d-wave superconductors.Comment: 4 pages, 3 figs; extended discussion of large-N spin representations,
added references; accepted for publication in PR
Ferromagnetism in the Periodic Anderson Model - a Modified Alloy Analogy
We introduce a new aproximation scheme for the periodic Anderson model (PAM).
The modified alloy approximation represents an optimum alloy approximation for
the strong coupling limit, which can be solved within the CPA-formalism.
Zero-temperature and finite-temperature phase diagrams are presented for the
PAM in the intermediate-valence regime. The diversity of magnetic properties
accessible by variation of the system parameters can be studied by means of
quasiparticle densities of states: The conduction band couples either ferro- or
antiferromagneticaly to the f-levels. A finite hybridization is a necessary
precondition for ferromagnetism. However, too strong hybridization generally
suppresses ferromagnetism, but can for certain system parameters also lead to a
semi-metallic state with unusual magnetic properties. By comparing with the
spectral density approximation, the influence of quasiparticle damping can be
examined.Comment: 20 pages, 13 figure
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