Reconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data

In this paper, I propose a technique for recovering quantum dynamical information from imaginary-time data via the resolution of a one-dimensional Hamburger moment problem. It is shown that the quantum autocorrelation functions are uniquely determined by and can be reconstructed from their sequence of derivatives at origin. A general class of reconstruction algorithms is then identified, according to Theorem 3. The technique is advocated as especially effective for a certain class of quantum problems in continuum space, for which only a few moments are necessary. For such problems, it is argued that the derivatives at origin can be evaluated by Monte Carlo simulations via estimators of finite variances in the limit of an infinite number of path variables. Finally, a maximum entropy inversion algorithm for the Hamburger moment problem is utilized to compute the quantum rate of reaction for a one-dimensional symmetric Eckart barrier.Comment: 15 pages, no figures, to appear in Phys. Rev.

Ground-State Dynamical Correlation Functions: An Approach from Density Matrix Renormalization Group Method

A numerical approach to ground-state dynamical correlation functions from Density Matrix Renormalization Group (DMRG) is developed. Using sum rules, moments of a dynamic correlation function can be calculated with DMRG, and with the moments the dynamic correlation function can be obtained by the maximum entropy method. We apply this method to one-dimensional spinless fermion system, which can be converted to the spin 1/2 Heisenberg model in a special case. The dynamical density-density correlation function is obtained.Comment: 11 pages, latex, 4 figure

Quasiparticle Band Structure and Density Functional Theory: Single-Particle Excitations and Band Gaps in Lattice Models

We compare the quasiparticle band structure for a model insulator obtained from the fluctuation exchange approximation (FEA) with the eigenvalues of the corresponding density functional theory (DFT) and local density approximation (LDA). The discontinuity in the exchange-correlation potential for this model is small and the FEA and DFT band structures are in good agreement. In contrast to conventional wisdom, the LDA for this model overestimates the size of the band gap. We argue that this is a consequence of an FEA self-energy that is strongly frequency dependent, but essentially local.Comment: 8 pages, and 5 figure

Two-band Fluctuation Exchange Study on the Superconductivity of β′\beta'-(BEDT-TTF)2_2ICl2_2 under High Pressure

We study the pressure dependence of the superconducting transition temperature of an organic superconductor $\beta'$-(BEDT-TTF)$_2$ICl$_2$ by applying the fluctuation exchange method to the Hubbard model on the original two-band lattice at 3/4-filling rather than the single band model in the strong dimerization limit. Our study is motivated by the fact that hopping parameters evaluated from a first-principles study suggest that the dimerization of the BEDT-TTF molecules is not so strong especially at high pressure. Solving the linearized Eliashberg's equation, a d$_{xy}$-wave-like superconducting state with realistic values of $T_c$ is obtained in a pressure regime somewhat higher than the actual experimental result. These results are similar to those obtained within the single band model in the previous study by Kino {\it et al}. We conclude that the resemblance to the dimer limit is due to a combination of a good Fermi surface nesting, a large density of states near the Fermi level, and a moderate dimerization, which cooperatively enhance electron correlation effects and also the superconducting $T_c$.Comment: 6 pages, 8 figure

Self-consistency over the charge-density in dynamical mean-field theory: a linear muffin-tin implementation and some physical implications

We present a simple implementation of the dynamical mean-field theory approach to the electronic structure of strongly correlated materials. This implementation achieves full self-consistency over the charge density, taking into account correlation-induced changes to the total charge density and effective Kohn-Sham Hamiltonian. A linear muffin-tin orbital basis-set is used, and the charge density is computed from moments of the many body momentum-distribution matrix. The calculation of the total energy is also considered, with a proper treatment of high-frequency tails of the Green's function and self-energy. The method is illustrated on two materials with well-localized 4f electrons, insulating cerium sesquioxide Ce2O3 and the gamma-phase of metallic cerium, using the Hubbard-I approximation to the dynamical mean-field self-energy. The momentum-integrated spectral function and momentum-resolved dispersion of the Hubbard bands are calculated, as well as the volume-dependence of the total energy. We show that full self-consistency over the charge density, taking into account its modification by strong correlations, can be important for the computation of both thermodynamical and spectral properties, particularly in the case of the oxide material.Comment: 20 pages, 6 figures (submitted in The Physical Review B

Phase Diagram of Superconductivity on the Anisotropic Triangular Lattice Hubbard Model

We study the electronic states of the anisotropic triangular lattice Hubbard model at half filling, which is a simple effective model for the organic superconducting $\kappa$-BEDT-TTF compounds. We treat the effect of the Coulomb interaction by the fluctuation exchange (FLEX) method, and obtain the phase diagram of this model for various sets of parameters. It is shown that the d-wave superconductivity is realized in the wide region of the phase diagram, next to the antiferromagnetic states. The obtained phase diagram explains the characters of the experimental results very well.Comment: 4 pages, 6 figs, submitted for publicatio

Dynamical Properties of a Haldane Gap Antiferromagnet

We study the dynamic spin correlation function of a spin one antiferromagnetic chain with easy-plane single-ion anisotropy. We use exact diagonalization by the Lancz\H os method for chains of lengths up to N=16 spins. We show that a single-mode approximation is an excellent description of the dynamical properties. A variational calculation allows us to clarify the nature of the excitations. The existence of a two-particle continuum near zero wavevector is clearly seen both in finite-size effects and in the dynamical structure factor. The recent neutron scattering experiments on the quasi-one-dimensional antiferromagnet NENP are fully explained by our results.Comment: 14 pages, SphT/92-135 plain tex with Postscript figures included. Postscipt file available by anonymous ftp at amoco.saclay.cea.fr by get pubs.spht/92-135.ps local_file (290 kb) or get pubs.spht/92-135.ps.Z local_file.Z (compressed - 120 kb

On the correct strong-coupling limit in the evolution from BCS superconductivity to Bose-Einstein condensation

We consider the problem of the crossover from BCS superconductivity to Bose-Einstein condensation in three dimensions for a system of fermions with an attractive interaction, for which we adopt the simplifying assumption of a suitably regularized point-contact interaction. We examine in a critical way the fermionic (self-consistent) T-matrix approximation which has been widely utilized in the literature to describe this crossover above the superconducting critical temperature, and show that it fails to yield the correct behaviour of the system in the strong-coupling limit, where composite bosons form as tightly bound fermion pairs. We then set up the correct approximation for a ``dilute'' system of composite bosons and show that an entire new class of diagrams has to be considered in the place of the fermionic T-matrix approximation for the self-energy. This new class of diagrams correctly describes both the weak- and strong-coupling limits, and consequently results into an improved interpolation scheme for the intermediate (crossover) region. In this context, we provide also a systematic mapping between the corresponding diagrammatic theories for the composite bosons and the constituent fermions. As a preliminary result to demonstrate the numerical effect of our new class of diagrams on physical quantities, we calculate the value of the scattering length for composite bosons in the strong-coupling limit and show that it is considerably modified with respect to the result obtained within the self-consistent fermionic T-matrix approximation.Comment: 25 pages, 14 figures included in pape

Image resonance in the many-body density of states at a metal surface

The electronic properties of a semi-infinite metal surface without a bulk gap are studied by a formalism that is able to account for the continuous spectrum of the system. The density of states at the surface is calculated within the GW approximation of many-body perturbation theory. We demonstrate the presence of an unoccupied surface resonance peaked at the position of the first image state. The resonance encompasses the whole Rydberg series of image states and cannot be resolved into individual peaks. Its origin is the shift in spectral weight when many-body correlation effects are taken into account