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, $1/r$ 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 $g$-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 $1/r$-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~$1/r$-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