128 research outputs found
Random phase approximation for multi-band Hubbard models
We derive the random-phase approximation for spin excitations in general
multi-band Hubbard models, starting from a collinear ferromagnetic Hartree-Fock
ground state. The results are compared with those of a recently introduced
variational many-body approach to spin-waves in itinerant ferromagnets. As we
exemplify for Hubbard models with one and two bands, the two approaches lead to
qualitatively different results. The discrepancies can be traced back to the
fact that the Hartree-Fock theory fails to describe properly the local moments
which naturally arise in a correlated-electron theory.Comment: 25 pages, 2 figure
Influence of Spin Wave Excitations on the Ferromagnetic Phase Diagram in the Hubbard-Model
The subject of the present paper is the theoretical description of collective
electronic excitations, i.e. spin waves, in the Hubbard-model. Starting with
the widely used Random-Phase-Approximation, which combines Hartree-Fock theory
with the summation of the two-particle ladder, we extend the theory to a more
sophisticated single particle approximation, namely the
Spectral-Density-Ansatz. Doing so we have to introduce a `screened`
Coulomb-interaction rather than the bare Hubbard-interaction in order to obtain
physically reasonable spinwave dispersions. The discussion following the
technical procedure shows that comparison of standard RPA with our new
approximation reduces the occurrence of a ferromagnetic phase further with
respect to the phase-diagrams delivered by the single particle theories.Comment: 8 pages, 9 figures, RevTex4, accepted for publication in Phys. Rev.
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
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
A Quantum Monte Carlo Method and Its Applications to Multi-Orbital Hubbard Models
We present a framework of an auxiliary field quantum Monte Carlo (QMC) method
for multi-orbital Hubbard models. Our formulation can be applied to a
Hamiltonian which includes terms for on-site Coulomb interaction for both
intra- and inter-orbitals, intra-site exchange interaction and energy
differences between orbitals. Based on our framework, we point out possible
ways to investigate various phase transitions such as metal-insulator, magnetic
and orbital order-disorder transitions without the minus sign problem. As an
application, a two-band model is investigated by the projection QMC method and
the ground state properties of this model are presented.Comment: 10 pages LaTeX including 2 PS figures, to appear in J.Phys.Soc.Jp
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
The Metal-Insulator Transition in the Doubly Degenerate Hubbard Model
A systematic study has been made on the metal-insulator (MI) transition of
the doubly degenerate Hubbard model (DHM) in the paramagnetic ground state, by
using the slave-boson mean-field theory which is equivalent to the Gutzwiller
approximation (GA). For the case of infinite electron-electron interactions, we
obtain the analytic solution, which becomes exact in the limit of infinite
spatial dimension. On the contrary, the finite-interaction case is investigated
by numerical methods with the use of the simple-cubic model with the
nearest-neighbor hopping. The mass-enhancement factor, , is shown to
increase divergently as one approaches the integer fillings (), at
which the MI transition takes place, being the total number of electrons.
The calculated dependence of is compared with the observed
specific-heat coefficient, , of which is reported
to significantly increase as approaches unity.Comment: Latex 16 pages, 10 ps figures included, published in J. Phys. Soc.
Jpn. with some minor modifications. ([email protected]
Phase diagram of orbital-selective Mott transitions at finite temperatures
Mott transitions in the two-orbital Hubbard model with different bandwidths
are investigated at finite temperatures. By means of the self-energy functional
approach, we discuss the stability of the intermediate phase with one orbital
localized and the other itinerant, which is caused by the orbital-selective
Mott transition (OSMT). It is shown that the OSMT realizes two different
coexistence regions at finite temperatures in accordance with the recent
results of Liebsch. We further find that the particularly interesting behavior
emerges around the special condition and J=0, which includes a new type
of the coexistence region with three distinct states. By systematically
changing the Hund coupling, we establish the global phase diagram to elucidate
the key role played by the Hund coupling on the Mott transitions.Comment: 4 pages, 6 figure
Formation of heavy quasiparticle state in two-band Hubbard model
A realization of heavy fermion state is investigated on the basis of two-band
Hubbard model. By means of the slave-boson mean-field approximation, it is
shown that for the intermediate electron density, n_e=1.5, the inter-band
Coulomb repulsion U strongly emphasizes initially small difference between
bands, and easily stabilizes integral valence in the lower band. As a result, a
strong renormalization takes place in the lower band and the mixing strength
between two bands. It gives rise to a sharp peak at the Fermi level in the
quasiparticle density of states, as that obtained in the periodic Anderson
model. In contrast to a simple insight that the Hund's-rule coupling J reduces
the characteristic energy, it turns out to be almost irrelevant to the
renormalization for J<U. The required conditions are suitable for LiV_2O_4, the
first observed heavy fermion compound in transition metal oxide.Comment: 5 pages, 4 figures, to be published in Phys. Rev.
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