Effects of spin fluctuations in the t-J model

Recent experiments on the Fermi surface and the electronic structure of the cuprate-supercondutors showed the importance of short range antiferromagnetic correlations for the physics in these systems. Theoretically, features like shadow bands were predicted and calculated mainly for the Hubbard model. In our approach we calculate an approximate selfenergy of the $t$-$J$ model. Solving the $U=\infty$ Hubbard model in the Dynamical Mean Field Theory (DMFT) yields a selfenergy that contains most of the local correlations as a starting point. Effects of the nearest neighbor spin interaction $J$ are then included in a heuristical manner. Formally like in $J$-perturbation theory all ring diagrams, with the single bubble assumed to be purely local, are summed to get a correction to the DMFT-self engergy This procedure causes new bands and can furnish strong deformation of quasiparticle bands. % Our results are finally compared with %former approaches to the Hubbard model.Comment: 3 Pages, Latex, 2 Postscript-Figures submitted to Physica

From Slater to Mott-Heisenberg physics: The antiferromagnetic phase of the Hubbard model

We study the optical conductivity of the one-band Hubbard model in the N\'eel state at half filling at T=0 using the dynamical mean-field theory. For small values of the Coulomb parameter clear signatures of a Slater insulator expected from a weak-coupling theory are found, while the strongly correlated system can be well described in terms of a Mott-Heisenberg picture. However, in contrast to the paramagnet, we do not find any evidence for a transition between these two limiting cases but rather a smooth crossover as a function of the Coulomb interaction.Comment: 8 pages, 9 figure

Spectral Properties and Bandstructure of Correlated Electron Systems

We present $\vec{k}$-dependent one-particle spectra and corresponding effective bandstructures for the $2d$ Hubbard model calculated within the dynamical molecular field theory (DMFT). This method has proven to yield highly nontrivial results for a variety of quantities but the question remains open to what extent it is applicable to relevant physical situations. To address this problem we compare our results for spectral functions to those obtained by QMC simulations. The good agreement supports our notion that the DMFT is indeed a sensible ansatz for correlated models even in to $d=2$.Comment: Paper presented at SCES '95, Sept. 27 - 30 1995, Goa. To be published in Physica B. 10 pages, figures include

A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models

We present a novel technique for the calculation of dynamical correlation functions of quantum impurity systems in equilibrium with Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain. In contrast to all previous methods, it does not suffer from overcounting of excitation. By construction, it always fulfills sum rules for spectral functions. Furthermore, it accurately reproduces local thermodynamic expectation values, such as occupancy and magnetization, obtained directly from the numerical renormalization group calculations.Comment: 13 pages, 7 figur

Conductivity of interacting spinless fermion systems via the high dimensional approach

Spinless fermions with repulsion are treated non-perturbatively by classifying the diagrams of the generating functional $\Phi$ in powers of the inverse lattice dimension $1/d$. The equations derived from the first two orders are evaluated on the one- and on the two-particle level. The order parameter of the AB-charge density wave (AB-CDW) occurring at larger interaction is calculated in $d=3$. The Bethe-Salpeter equation is evaluated for the conductivity \sigma(\om) which is found to have two peaks within the energy gap $2\Delta$ in the AB-CDW: a remnant of the Drude peak and an excitonic resonance. Unexpectedly, $\sigma_{\rm\scriptscriptstyle DC}$ does not vanish for $T\to 0$Comment: Latex, 4 page

Magnetism and Phase Separation in the Ground State of the Hubbard Model

We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilise a Neel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed.Comment: 9 pages, 11 figure

Half-filled Hubbard Model on a Bethe lattice with next-nearest neighbor hopping

We study the interplay between N\'eel-antiferromagnetism and the paramagnetic metal-insulator-transition (PMIT) on a Bethe lattice with nearest and next-nearest eighbor hopping $t_1$ and $t_2$. We concentrate in this paper on the situation at half-filling. For $t_2/t_1\to 1$ the PMIT outgrows the antiferromagnetic phase and shows a scenario similar to V$_2$O$_3$. In this parameter regime we also observe a novel magnetic phase.Comment: 8 pages, 10 figure

On the Analyticity of Solutions in the Dynamical Mean-Field Theory

The unphysical solutions of the periodic Anderson model obtained by H. Keiter and T. Leuders [Europhys. Lett. 49, 801(2000)] in dynamical mean-field theory (DMFT) are shown to result from the author's restricted choice of the functional form of the solution, leading to a violation of the analytic properties of the exact solution. By contrast, iterative solutions of the self-consistency condition within the DMFT obtained by techniques which preserve the correct analytic properties of the exact solution (e.g., quantum Monte-Carlo simulations or the numerical renormalization group) always lead to physical solutions.Comment: 4 pages, 1 figur