1,517 research outputs found
Temperature and Dimensionality Dependences of Optical Absorption Spectra in Mott Insulators
We investigate the temperature dependence of optical absorption spectra of
one-dimensional (1D) and two-dimensional (2D) Mott insulators by using an
effective model in the strong-coupling limit of a half-filed Hubbard model. In
the numerically exact diagonalization calculations on finite-size clusters, we
find that in 1D the energy position of the absorption edge is almost
independent of temperature, while in 2D the edge position shifts to lower
energy with increasing temperature. The different temperature dependence
between 1D and 2D is attributed to the difference of the coupling of the charge
and spin degrees of freedom. The implications of the results on experiments are
discussed in terms of the dimensionality dependence.Comment: 5 pages, 4 figure
Equivalence of Gutzwiller and slave-boson mean-field theories for multi-band Hubbard models
We demonstrate that a recently introduced slave-boson mean-field theory is
equivalent to our Gutzwiller theory for multi-band Hubbard models with general
onsite interactions. We relate the different objects that appear in both
approaches at zero temperature and discuss the limitations of both methods.Comment: 4 page
Thermodynamics of the one-dimensional half-filled Hubbard model in the spin-disordered regime
We analyze the Thermodynamic Bethe Ansatz equations of the one-dimensional
half-filled Hubbard model in the "spin-disordered regime", which is
characterized by the temperature being much larger than the magnetic energy
scale but small compared to the Mott-Hubbard gap. In this regime the
thermodynamics of the Hubbard model can be thought of in terms of gapped
charged excitations with an effective dispersion and spin degrees of freedom
that only contribute entropically. In particular, the internal energy and the
effective dispersion become essentially independent of temperature. An
interpretation of this regime in terms of a putative interacting-electron
system at zero temperature leads to a metal-insulator transition at a finite
interaction strength above which the gap opens linearly. We relate these
observations to studies of the Mott-Hubbard transition in the limit of infinite
dimensions.Comment: 15 pages, 3 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
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.
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
Charge and Spin Gap Formation in Exactly Solvable Hubbard Chains with Long-Rang Hopping
We discuss the transition from a metal to charge or spin insulating phases
characterized by the opening of a gap in the charge or spin excitation spectra,
respectively. These transitions are addressed within the context of two exactly
solvable Hubbard and tJ chains with long range, hopping. We discuss the
specific heat, compressibility, and magnetic susceptibility of these models as
a function of temperature, band filling, and interaction strength. We then use
conformal field theory techniques to extract ground state correlation
functions. Finally, by employing the -ology analysis we show that the charge
insulator transition is accompanied by an infinite discontinuity in the Drude
weight of the electrical conductivity. While the magnetic properties of these
models reflect the genuine features of strongly correlated electron systems,
the charge transport properties, especially near the Mott-Hubbard transition,
display a non-generic behavior.Comment: 47 pages, REVTEX 3.0, 14 postscript figures available form
[email protected] (submitted using the figures-command
The Anderson impurity model with a narrow-band host: from orbital physics to the Kondo effect
A particle-hole symmetric Anderson impurity model with a metallic host of
narrow bandwidth is studied within the framework of the local moment approach.
The resultant single-particle spectra are compared to unrestricted
Hartree-Fock, second order perturbation theory about the noninteracting limit,
and Lanczos spectra by Hofstetter and Kehrein. Rather accurate analytical
results explain the spectral evolution over almost the entire range of
interactions. These encompass, in particular, a rationale for the four-peak
structure observed in the low-energy sector of the Lanczos spectra in the
moderate-coupling regime. In weak coupling, the spectral evolution is governed
by orbital effects, while in the strong coupling Kondo limit, the model is
shown to connect smoothly to the generic Anderson impurity with a flat and
infinitely wide hybridization band.Comment: 17 pages, 7 figure
Quantum Antiferromagnetism of Fermions in Optical Lattices with Half-filled p-band
We study Fermi gases in a three-dimensional optical lattice with five
fermions per site, i.e. the s-band is completely filled and the p-band with
three-fold degeneracy is half filled. We show that, for repulsive interaction
between fermions, the system will exhibit spin-3/2 antiferromagnetic order at
low temperature. This conclusion is obtained in strong interaction regime by
strong coupling expansion which yields an isotropic spin-3/2 Heisenberg model,
and also in weak interaction regime by Hatree-Fock mean-field theory and
analysis of Fermi surface nesting. We show that the critical temperature for
this antiferromagnetism of a p-band Mott insulator is about two orders of
magnitudes higher than that of an -band Mott insulator, which is close to
the lowest temperature attainable nowadays
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