865 research outputs found
Random dispersion approximation for the Hubbard model
We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard
transition in the Hubbard model at half band filling. The RDA becomes exact for
the Hubbard model in infinite dimensions. We implement the RDA on finite chains
and employ the Lanczos exact diagonalization method in real space to calculate
the ground-state energy, the average double occupancy, the charge gap, the
momentum distribution, and the quasi-particle weight. We find a satisfactory
agreement with perturbative results in the weak- and strong-coupling limits. A
straightforward extrapolation of the RDA data for lattice results in
a continuous Mott-Hubbard transition at . We discuss the
significance of a possible signature of a coexistence region between insulating
and metallic ground states in the RDA that would correspond to the scenario of
a discontinuous Mott-Hubbard transition as found in numerical investigations of
the Dynamical Mean-Field Theory for the Hubbard model.Comment: 10 pages, 11 figure
Perturbation theory for optical excitations in the one-dimensional extended Peierls--Hubbard model
For the one-dimensional, extended Peierls--Hubbard model we calculate
analytically the ground-state energy and the single-particle gap to second
order in the Coulomb interaction for a given lattice dimerization. The
comparison with numerically exact data from the Density-Matrix Renormalization
Group shows that the ground-state energy is quantitatively reliable for Coulomb
parameters as large as the band width. The single-particle gap can almost
triple from its bare Peierls value before substantial deviations appear. For
the calculation of the dominant optical excitations, we follow two approaches.
In Wannier theory, we perturb the Wannier exciton states to second order. In
two-step perturbation theory, similar in spirit to the GW-BSE approach, we form
excitons from dressed electron-hole excitations. We find the Wannier approach
to be superior to the two-step perturbation theory. For singlet excitons,
Wannier theory is applicable up to Coulomb parameters as large as half band
width. For triplet excitons, second-order perturbation theory quickly fails
completely.Comment: 32 pages, 12 figures, submtted to JSTA
Orbital-selective Mott-Hubbard transition in the two-band Hubbard model
Recent advances in the field of quantum Monte Carlo simulations for impurity
problems allow --within dynamical mean field theory-- for a more thorough
investigation of the two-band Hubbard model with narrow/wide band and
SU(2)-symmetric Hund's exchange. The nature of this transition has been
controversial, and we establish that an orbital-selective Mott-Hubbard
transition exists. Thereby, the wide band still shows metallic behavior after
the narrow band became insulating -not a pseudogap as for an Ising Hund's
exchange. The coexistence of two solutions with metallic wide band and
insulating or metallic narrow band indicates, in general, first-order
transitions.Comment: 4 pages, 3 figures; 2nd version as published in Phys. Rev. B (R);
minor corrections, putting more emphasis on differences in spectra when
comparing SU(2) and Ising Hund's exchang
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.
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.
Dynamical Mean-Field Theory - from Quantum Impurity Physics to Lattice Problems
Since the first investigation of the Hubbard model in the limit of infinite
dimensions by Metzner and Vollhardt, dynamical mean-field theory (DMFT) has
become a very powerful tool for the investigation of lattice models of
correlated electrons. In DMFT the lattice model is mapped on an effective
quantum impurity model in a bath which has to be determined self-consistently.
This approach lead to a significant progress in our understanding of typical
correlation problems such as the Mott transition; furthermore, the combination
of DMFT with ab-initio methods now allows for a realistic treatment of
correlated materials. The focus of these lecture notes is on the relation
between quantum impurity physics and the physics of lattice models within DMFT.
Issues such as the observability of impurity quantum phase transitions in the
corresponding lattice models are discussed in detail.Comment: 18 pages, 5 figures, invited paper for the Proceedings of the "3rd
International Summer School on Strongly Correlated Systems, Debrecen, 2004
Cluster approach study of intersite electron correlations in pyrochlore and checkerboard lattices
To treat effects of electron correlations in geometrically frustrated
pyrochlore and checkerboard lattices, an extended single-orbital Hubbard model
with nearest neighbor hopping and Coulomb repulsion is
applied. Infinite on-site repulsion, , is assumed, thus double
occupancies of sites are forbidden completely in the present study. A
variational Gutzwiller type approach is extended to examine correlations due to
short-range interaction and a cluster approximation is developed to
evaluate a variational ground state energy of the system. Obtained analytically
in a special case of quarter band filling appropriate to LiVO, the
resulting simple expression describes the ground state energy in the regime of
intermediate and strong coupling . Like in the Brinkman-Rice theory based on
the standard Gutzwiller approach to the Hubbard model, the mean value of the
kinetic energy is shown to be reduced strongly as the coupling approaches a
critical value . This finding may contribute to explaining the observed
heavy fermion behavior in LiVO
Strong-coupling approach to the Mott--Hubbard insulator on a Bethe lattice in Dynamical Mean-Field Theory
We calculate the Hubbard bands for the half-filled Hubbard model on a Bethe
lattice with infinite coordination number up to and including third order in
the inverse Hubbard interaction. We employ the Kato--Takahashi perturbation
theory to solve the self-consistency equation of the Dynamical Mean-Field
Theory analytically for the single-impurity Anderson model in multi-chain
geometry. The weight of the secondary Hubbard sub-bands is of fourth order so
that the two-chain geometry is sufficient for our study. Even close to the
Mott--Hubbard transition, our results for the Mott--Hubbard gap agree very well
with those from numerical Dynamical Density-Matrix Renormalization Group
(DDMRG) calculations. The density of states of the lower Hubbard band also
agrees very well with DDMRG data, apart from a resonance contribution at the
upper band edge which cannot be reproduced in low-order perturbation theory.Comment: 40 pages, 7 figure
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