830 research outputs found
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.
Ground-state phase diagram of a half-filled one-dimensional extended Hubbard model
The density-matrix renormalization group is used to study the phase diagram
of the one-dimensional half-filled Hubbard model with on-site (U) and
nearest-neighbor (V) repulsion, and hopping t. A critical line V_c(U)
approximately equal to U/2 separates a Mott insulating phase from a
charge-density-wave phase. The formation of bound charge excitations for V > 2t
changes the phase transition from continuous to first order at a tricritical
point U_t = 3.7t, V_t=2t. A frustrating effective antiferromagnetic spin
coupling induces a bond-order-wave phase on the critical line V_c(U) for U_t <
U < 7-8 t.Comment: 4 pages (REVTEX 4), 3 EPS figures, shorter abstract, text and
references modifie
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
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
Local Electronic Correlation at the Two-Particle Level
Electronic correlated systems are often well described by dynamical mean
field theory (DMFT). While DMFT studies have mainly focused hitherto on
one-particle properties, valuable information is also enclosed into local
two-particle Green's functions and vertices. They represent the main ingredient
to compute momentum-dependent response functions at the DMFT level and to treat
non-local spatial correlations at all length scales by means of diagrammatic
extensions of DMFT. The aim of this paper is to present a DMFT analysis of the
local reducible and irreducible two-particle vertex functions for the Hubbard
model in the context of an unified diagrammatic formalism. An interpretation of
the observed frequency structures is also given in terms of perturbation
theory, of the comparison with the atomic limit, and of the mapping onto the
attractive Hubbard model.Comment: 29 pages, 26 Figures. Accepted for publication in Phys. Rev.
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