799 research outputs found
Gutzwiller variational theory for the Hubbard model with attractive interaction
We investigate the electronic and superconducting properties of a negative-U
Hubbard model. For this purpose we evaluate a recently introduced variational
theory based on Gutzwiller-correlated BCS wave functions. We find significant
differences between our approach and standard BCS theory, especially for the
superconducting gap. For small values of , we derive analytical
expressions for the order parameter and the superconducting gap which we
compare to exact results from perturbation theory.Comment: 10 pages, 2 figure
Comparison of Variational Approaches for the Exactly Solvable 1/r-Hubbard Chain
We study Hartree-Fock, Gutzwiller, Baeriswyl, and combined
Gutzwiller-Baeriswyl wave functions for the exactly solvable one-dimensional
-Hubbard model. We find that none of these variational wave functions is
able to correctly reproduce the physics of the metal-to-insulator transition
which occurs in the model for half-filled bands when the interaction strength
equals the bandwidth. The many-particle problem to calculate the variational
ground state energy for the Baeriswyl and combined Gutzwiller-Baeriswyl wave
function is exactly solved for the~-Hubbard model. The latter wave
function becomes exact both for small and large interaction strength, but it
incorrectly predicts the metal-to-insulator transition to happen at infinitely
strong interactions. We conclude that neither Hartree-Fock nor Jastrow-type
wave functions yield reliable predictions on zero temperature phase transitions
in low-dimensional, i.e., charge-spin separated systems.Comment: 23 pages + 3 figures available on request; LaTeX under REVTeX 3.
Quantum phases in mixtures of fermionic atoms
A mixture of spin-polarized light and heavy fermionic atoms on a finite size
2D optical lattice is considered at various temperatures and values of the
coupling between the two atomic species. In the case, where the heavy atoms are
immobile in comparison to the light atoms, this system can be seen as a
correlated binary alloy related to the Falicov-Kimball model. The heavy atoms
represent a scattering environment for the light atoms. The distributions of
the binary alloy are discussed in terms of strong- and weak-coupling
expansions. We further present numerical results for the intermediate
interaction regime and for the density of states of the light particles. The
numerical approach is based on a combination of a Monte-Carlo simulation and an
exact diagonalization method. We find that the scattering by the correlated
heavy atoms can open a gap in the spectrum of the light atoms, either for
strong interaction or small temperatures.Comment: 15 pages, 8 figure
Application of the Density Matrix Renormalization Group in momentum space
We investigate the application of the Density Matrix Renormalization Group
(DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional
models with dispersion relations corresponding to nearest-neighbor hopping and
hopping and the two-dimensional model with isotropic nearest-neighbor
hopping. By comparing with the exact solutions for both one-dimensional models
and with exact diagonalization in two dimensions, we first investigate the
convergence of the ground-state energy. We find variational convergence of the
energy with the number of states kept for all models and parameter sets. In
contrast to the real-space algorithm, the accuracy becomes rapidly worse with
increasing interaction and is not significantly better at half filling. We
compare the results for different dispersion relations at fixed interaction
strength over bandwidth and find that extending the range of the hopping in one
dimension has little effect, but that changing the dimensionality from one to
two leads to lower accuracy at weak to moderate interaction strength. In the
one-dimensional models at half-filling, we also investigate the behavior of the
single-particle gap, the dispersion of spinon excitations, and the momentum
distribution function. For the single-particle gap, we find that proper
extrapolation in the number of states kept is important. For the spinon
dispersion, we find that good agreement with the exact forms can be achieved at
weak coupling if the large momentum-dependent finite-size effects are taken
into account for nearest-neighbor hopping. For the momentum distribution, we
compare with various weak-coupling and strong-coupling approximations and
discuss the importance of finite-size effects as well as the accuracy of the
DMRG.Comment: 15 pages, 11 eps figures, revtex
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
Exact analytic results for the Gutzwiller wave function with finite magnetization
We present analytic results for ground-state properties of Hubbard-type
models in terms of the Gutzwiller variational wave function with non-zero
values of the magnetization m. In dimension D=1 approximation-free evaluations
are made possible by appropriate canonical transformations and an analysis of
Umklapp processes. We calculate the double occupation and the momentum
distribution, as well as its discontinuity at the Fermi surface, for arbitrary
values of the interaction parameter g, density n, and magnetization m. These
quantities determine the expectation value of the one-dimensional Hubbard
Hamiltonian for any symmetric, monotonically increasing dispersion epsilon_k.
In particular for nearest-neighbor hopping and densities away from half filling
the Gutzwiller wave function is found to predict ferromagnetic behavior for
sufficiently large interaction U.Comment: REVTeX 4, 32 pages, 8 figure
Optical excitations of Peierls-Mott insulators with bond disorder
The density-matrix renormalization group (DMRG) is employed to calculate
optical properties of the half-filled Hubbard model with nearest-neighbor
interactions. In order to model the optical excitations of oligoenes, a Peierls
dimerization is included whose strength for the single bonds may fluctuate.
Systems with up to 100 electrons are investigated, their wave functions are
analyzed, and relevant length-scales for the low-lying optical excitations are
identified. The presented approach provides a concise picture for the size
dependence of the optical absorption in oligoenes.Comment: 12 pages, 13 figures, submitted to Phys. Rev.
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
Correlated hopping of electrons: Effect on the Brinkman-Rice transition and the stability of metallic ferromagnetism
We study the Hubbard model with bond-charge interaction (`correlated
hopping') in terms of the Gutzwiller wave function. We show how to express the
Gutzwiller expectation value of the bond-charge interaction in terms of the
correlated momentum-space occupation. This relation is valid in all spatial
dimensions. We find that in infinite dimensions, where the Gutzwiller
approximation becomes exact, the bond-charge interaction lowers the critical
Hubbard interaction for the Brinkman-Rice metal-insulator transition. The
bond-charge interaction also favors ferromagnetic transitions, especially if
the density of states is not symmetric and has a large spectral weight below
the Fermi energy.Comment: 5 pages, 3 figures; minor changes, published versio
Optical absorption of non-interacting tight-binding electrons in a Peierls-distorted chain at half band-filling
In this first of three articles on the optical absorption of electrons in
half-filled Peierls-distorted chains we present analytical results for
non-interacting tight-binding electrons. We carefully derive explicit
expressions for the current operator, the dipole transition matrix elements,
and the optical absorption for electrons with a cosine dispersion relation of
band width and dimerization parameter . New correction
(``''-)terms to the current operator are identified. A broad band-to-band
transition is found in the frequency range whose shape
is determined by the joint density of states for the upper and lower Peierls
subbands and the strong momentum dependence of the transition matrix elements.Comment: 17 pages REVTEX 3.0, 2 postscript figures; hardcopy versions before
May 96 are obsolete; accepted for publication in The Philosophical Magazine
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