1,665 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.
Self-energy corrections to anisotropic Fermi surfaces
The electron-electron interactions affect the low-energy excitations of an
electronic system and induce deformations of the Fermi surface. These effects
are especially important in anisotropic materials with strong correlations,
such as copper oxides superconductors or ruthenates. Here we analyze the
deformations produced by electronic correlations in the Fermi surface of
anisotropic two-dimensional systems, treating the regular and singular regions
of the Fermi surface on the same footing. Simple analytical expressions are
obtained for the corrections, based on local features of the Fermi surface. It
is shown that, even for weak local interactions, the behavior of the
self-energy is non trivial, showing a momentum dependence and a self-consistent
interplay with the Fermi surface topology. Results are compared to experimental
observations and to other theoretical results.Comment: 13 pages, 10 figure
Strong-Coupling Expansion for the Hubbard Model
A strong-coupling expansion for models of correlated electrons in any
dimension is presented. The method is applied to the Hubbard model in
dimensions and compared with numerical results in . Third order expansion
of the Green function suffices to exhibit both the Mott metal-insulator
transition and a low-temperature regime where antiferromagnetic correlations
are strong. It is predicted that some of the weak photoemission signals
observed in one-dimensional systems such as should become stronger as
temperature increases away from the spin-charge separated state.Comment: 4 pages, RevTex, 3 epsf figures include
Multi-band Gutzwiller wave functions for general on-site interactions
We introduce Gutzwiller wave functions for multi-band models with general
on-site Coulomb interactions. As these wave functions employ correlators for
the exact atomic eigenstates they are exact both in the non-interacting and in
the atomic limit. We evaluate them in infinite lattice dimensions for all
interaction strengths without any restrictions on the structure of the
Hamiltonian or the symmetry of the ground state. The results for the
ground-state energy allow us to derive an effective one-electron Hamiltonian
for Landau quasi-particles, applicable for finite temperatures and frequencies
within the Fermi-liquid regime. As applications for a two-band model we study
the Brinkman-Rice metal-to-insulator transition at half band-filling, and the
transition to itinerant ferromagnetism for two specific fillings, at and close
to a peak in the density of states of the non-interacting system. Our new
results significantly differ from those for earlier Gutzwiller wave functions
where only density-type interactions were included. When the correct spin
symmetries for the two-electron states are taken into account, the importance
of the Hund's-rule exchange interaction is even more pronounced and leads to
paramagnetic metallic ground states with large local magnetic moments.
Ferromagnetism requires fairly large interaction strengths, and the resulting
ferromagnetic state is a strongly correlated metal.Comment: 37 pages, 10 figures; accepted for publication in Phys. Rev. B 57
(March 15, 1998
Inhomogeneous Gutzwiller approximation with random phase fluctuations for the Hubbard model
We present a detailed study of the time-dependent Gutzwiller approximation
for the Hubbard model. The formalism, labelled GA+RPA, allows us to compute
random-phase approximation-like (RPA) fluctuations on top of the Gutzwiller
approximation (GA). No restrictions are imposed on the charge and spin
configurations which makes the method suitable for the calculation of linear
excitations around symmetry-broken solutions. Well-behaved sum rules are obeyed
as in the Hartree-Fock (HF) plus RPA approach. Analytical results for a
two-site model and numerical results for charge-charge and current-current
dynamical correlation functions in one and two dimensions are compared with
exact and HF+RPA results, supporting the much better performance of GA+RPA with
respect to conventional HF+RPA theory.Comment: 14 pages, 6 figure
Time-dependent Gutzwiller approximation for the Hubbard model
We develop a time-dependent Gutzwiller approximation (GA) for the Hubbard
model analogous to the time-dependent Hartree-Fock (HF) method. The formalism
incorporates ground state correlations of the random phase approximation (RPA)
type beyond the GA. Static quantities like ground state energy and double
occupancy are in excellent agreement with exact results in one dimension up to
moderate coupling and in two dimensions for all couplings. We find a
substantial improvement over traditional GA and HF+RPA treatments. Dynamical
correlation functions can be easily computed and are also substantially better
than HF+RPA ones and obey well behaved sum rules.Comment: 4 pages, 2 figure
Mott-Hubbard transition in infinite dimensions
We calculate the zero-temperature gap and quasiparticle weight of the
half-filled Hubbard model with a random dispersion relation. After
extrapolation to the thermodynamic limit, we obtain reliable bounds on these
quantities for the Hubbard model in infinite dimensions. Our data indicate that
the Mott-Hubbard transition is continuous, i.e., that the quasiparticle weight
becomes zero at the same critical interaction strength at which the gap opens.Comment: 4 pages, RevTeX, 5 figures included with epsfig Final version for
PRL, includes L=14 dat
Slave-Boson Mean-Field Theory of the Antiferromagnetic State in the Doubly Degenerate Hubbard Model - the Half-Filled Case -
The antiferromagnetic ground state of the half-filled Hubbard model with the
doubly degenerate orbital has been studied by using the slave-boson mean-field
theory which was previously proposed by the present author. Numerical
calculations for the simple cubic model have shown that the metal-insulator
transition does not take place except at the vanishing interaction point, in
strong contrast with its paramagnetic solution. The energy gap in the density
of states of the antiferromagnetic insulator is much reduced by the effect of
electron correlation. The exchange interaction plays an important role in
the antiferromagnetism: although for the sublattice magnetic moment
in our theory is fairly smaller than obtained in the Hartree-Fock
approximation, for (: the Coulomb interaction) is increased
to become comparable to . Surprisingly, the antiferromagnetic state is
easily destroyed if a small, negative exchange interaction () is
introduced.Comment: Latex 18 pages, 12 figures available on request to
[email protected] Note: published in Phys. Rev. B with some minor
modification
Quantum Monte Carlo calculation of the finite temperature Mott-Hubbard transition
We present clear numerical evidence for the coexistence of metallic and
insulating dynamical mean field theory(DMFT) solutions in a half-filled
single-band Hubbard model with bare semicircular density of states at finite
temperatures. Quantum Monte Carlo(QMC) method is used to solve the DMFT
equations. We discuss important technical aspects of the DMFT-QMC which need to
be taken into account in order to obtain the reliable results near the
coexistence region. Among them are the critical slowing down of the iterative
solutions near phase boundaries, the convergence criteria for the DMFT
iterations, the interpolation of the discretized Green's function and the
reduction of QMC statistical and systematic errors. Comparison of our results
with those of other numerical methods is presented in a phase diagram.Comment: 4 pages, 5 figure
Renormalization group analysis of the 2D Hubbard model
Salmhofer [Commun. Math. Phys. 194, 249 (1998)] has recently developed a new
renormalization group method for interacting Fermi systems, where the complete
flow from the bare action of a microscopic model to the effective low-energy
action, as a function of a continuously decreasing infrared cutoff, is given by
a differential flow equation which is local in the flow parameter. We apply
this approach to the repulsive two-dimensional Hubbard model with nearest and
next-nearest neighbor hopping amplitudes. The flow equation for the effective
interaction is evaluated numerically on 1-loop level. The effective
interactions diverge at a finite energy scale which is exponentially small for
small bare interactions. To analyze the nature of the instabilities signalled
by the diverging interactions we extend Salmhofers renormalization group for
the calculation of susceptibilities. We compute the singlet superconducting
susceptibilities for various pairing symmetries and also charge and spin
density susceptibilities. Depending on the choice of the model parameters
(hopping amplitudes, interaction strength and band-filling) we find
commensurate and incommensurate antiferromagnetic instabilities or d-wave
superconductivity as leading instability. We present the resulting phase
diagram in the vicinity of half-filling and also results for the density
dependence of the critical energy scale.Comment: 16 pages, RevTeX, 16 eps figure
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