U. Brandt

Exact results for the distribution of thef-level ground state occupation in the spinless Falicov-Kimball model

We present sharp upper and lower bounds for the ground state energy of the spinless Falicov-Kimball model, leading to rigorous results for a special choice of parameters. In this ‘symmetric’ case we are able to give the exactf-level occupation pattern for a square lattice. A superstructure occurs, leading to a metal-insulator transition.

Thermodynamics of the Falicov-Kimball model in large dimensions II

In a former paper we presented the exact solution of the Falicov-Kimball-model in large dimensions and showed the existence of phase transitions for certain parameter combinations, especially for the symmetric case. In this contribution we investigate the conditions for transitions apart from the symmetric case and show that the phase following the homogeneous high temperature phase will have chessboard symmetry if the transition is a continuous charge density transition. The corresponding phase diagrams are shown as well as results on the order parameter of the chessboard phase.

Exact results for the dynamics of one-dimensional spin-systems

In this contribution we discuss the spin-dynamics of anisotropic one-dimensional spin 1/2X-Y-chains in a magnetic field. For special values of the parameters we solve the equation of motion for several spin-operators exactly. These results we use to calculate longitudinal and transverse dynamical correlation functions at temperatureT=∞, for an Ising chain in a transverse field also the first-order high-temperature correction is given.

Free energy of the Falicov-Kimball model in large dimensions

We show how to calculate the free energy of the spinless Falicov Kimball model exactly in the limit of infinite dimensions, and do it explicitly for the homogeneous and the chessboard phase. By comparing the free energies for those two cases we study the transitions between the pure phases, and by looking for concavities in the course of the free energy as a function of the meanf-particle density we examine the possibility of phase segregation.

Ground state properties of a spinless Falicov-Kimball model; additional features

We have studied some energetic and structural ground state properties of a spinless Falicov-Kimball model. Using a method based on “Tchebycheff-Markoff inequalities”, we have calculated sharp upper and lower bounds for the ground state energy. These calculations lead to rigorous results for a special range of parameters, where we are able to give the exactf-level occupation pattern for a square lattice. The results for the “symmetric” case, where a superstructure occurs leading to a metal-insulator transition, have already been published. In this paper we present some additional results also for the “unsymmetric case” and study valence-transitions for fixed particle-number.

The transverse correlation function of anisotropicX—Y-chains: Exact results atT=∞

In this contribution we present exact results for the transverse dynamical correlation function of anisotropic spin 1/2X—Y-chains in the presence of magnetic fields at temperatureT=∞. Our results are obtained by an application of a new theory of block-Toeplitz determinants also developed in this paper.

Ground states of extended Hubbard models in the atomic limit

The possible ground states of an extended Hubbard model in the atomic limit, augmented by an additional nearest neighbour Ising-like interaction and an external magnetic field, are rigorously determined for arbitrary values of the coupling parameters and arbitrary chemical potential. The method used requires only simple convexity arguments and the examination of all possible configurations of small clusters of lattice sites, which may be done by computer. The results are valid for all lattices ofAB type (two interpenetrating sublattices). The type of order found are ferromagnetic, antiferromagnetic, and charge density wave. Perturbation theory suggests that for finite band width there may be a state showing both a charge density wave and ferromagnetic order.

Thef-electron spectrum of the spinless Falicov-Kimball model in large dimensions

We present the exact solution of the imaginary and real time Greens function of the localized electrons of the spinless Falicov-Kimball model for large dimensions. With these functions we calculate upper and lower bounds for the integrated spectral function as well as the spectral function.

New phase in a spin-1/2 Falicov-Kimball model

In this investigation we present exact results on the spin-1/2 Falicov-Kimball model. We obtain ground-state results for arbitrary dimensions using the method of in-equalities as well as results on the thermodynamics for large dimensions. As a new feature (not possible in a spinless model) we obtain a transition (which may be discontinuous) into a new state with a high density of pairs of thef-electrons.

Ground States of the Triangular Ising Model with Two- and Three-Spin Interactions

The possible ground state spin configurations of an Ising model on a plane triangular lattice are investigated. The model incorporates competing interactions between spins at nearest and next-nearest neighbour sites as well as a coupling between three spins at the vertices of a nearest-neighbour triangle, and an external magnetic field. Models of this type are frequently used to describe the structures of adsorbate layers on hexagonal substrates. The analysis is based on linear inequalities involving the magnetization, two- and three-spin correlations, and on simple convexity arguments. Part of the inequalities needed are proved with the aid of a computer. For vanishing three-spin coupling the results of earlier studies are confirmed; in addition, the resulting seven topologically distinct structures are shown to be unique. Two of these structures are energetically degenerate; the degeneracy cannot be lifted by any further two-spin interaction. For nonzero three-spin coupling only an “almost complete” solution is given, involving four additional spin configurations. The “ground state phase diagrams” are discussed.