1,335 research outputs found
Ground state of the frustrated Hubbard model within DMFT: energetics of Mott insulator and metal from ePT and QMC
We present a new method, ePT, for extrapolating few known coefficients of a
perturbative expansion. Controlled by comparisons with numerically exact
quantum Monte Carlo (QMC) results, 10th order strong-coupling perturbation
theory (PT) for the Hubbard model on the Bethe lattice is reliably extrapolated
to infinite order. Within dynamical mean-field theory (DMFT), we obtain
continuous estimates of energy E and double occupancy D with unprecedented
precision O(10^{-5}) for the Mott insulator above its stability edge
U_{c1}=4.78 as well as critical exponents. In addition, we derive corresponding
precise estimates for E and D in the metallic ground state from extensive
low-temperature QMC simulations using a fit to weak-coupling PT while enforcing
thermodynamic consistency.Comment: 2 pages, 5 figures, submitted to SCES '0
Sinks in Acyclic Orientations of Graphs
Greene and Zaslavsky proved that the number of acyclic orientations of a
graph with a unique sink is, up to sign, the linear coefficient of the
chromatic polynomial. We give three new proofs of this result using pure
induction, noncommutative symmetric functions, and an algorithmic bijection.Comment: 17 pages, 1 figur
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
Optical conductivity of the one-dimensional dimerized Hubbard model at quarter filling
We investigate the optical conductivity in the Mott insulating phase of the
one-dimensional extended Hubbard model with alternating hopping terms
(dimerization) at quarter band filling. Optical spectra are calculated for the
various parameter regimes using the dynamical density-matrix renormalization
group method. The study of limiting cases allows us to explain the various
structures found numerically in the optical conductivity of this model. Our
calculations show that the dimerization and the nearest-neighbor repulsion
determine the main features of the spectrum. The on-site repulsion plays only a
secondary role. We discuss the consequences of our results for the theory of
the optical conductivity in the Bechgaard salts.Comment: 11 pages and 12 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.
Spectral function of the one-dimensional Hubbard model away from half filling
We calculate the photoemission spectral function of the one-dimensional
Hubbard model away from half filling using the dynamical density matrix
renormalization group method. An approach for calculating momentum-dependent
quantities in finite open chains is presented. Comparison with exact Bethe
Ansatz results demonstrates the unprecedented accuracy of our method. Our
results show that the photoemission spectrum of the quasi-one-dimensional
conductor TTF-TCNQ provides evidence for spin-charge separation on the scale of
the conduction band width.Comment: REVTEX, 4 pages including 4 EPS figures (changed); correct chemical
potential used to define excitation energies in figures and tex
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
Brueckner-Goldstone perturbation theory for the half-filled Hubbard model in infinite dimensions
We use Brueckner-Goldstone perturbation theory to calculate the ground-state
energy of the half-filled Hubbard model in infinite dimensions up to fourth
order in the Hubbard interaction. We obtain the momentum distribution as a
functional derivative of the ground-state energy with respect to the bare
dispersion relation. The resulting expressions agree with those from
Rayleigh-Schroedinger perturbation theory. Our results for the momentum
distribution and the quasi-particle weight agree very well with those obtained
earlier from Feynman-Dyson perturbation theory for the single-particle
self-energy. We give the correct fourth-order coefficient in the ground-state
energy which was not calculated accurately enough from Feynman-Dyson theory due
to the insufficient accuracy of the data for the self-energy, and find a good
agreement with recent estimates from Quantum Monte-Carlo calculations.Comment: 15 pages, 8 fugures, submitted to JSTA
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
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