E. Müller-Hartmann

Correlated fermions on a lattice in high dimensions

The limit of infinite dimension of the Hubbard model was recently introduced by Metzner and Vollhardt as a new type of model with interesting implications. In the present paper the same limit is applied to a family of lattice fermion models with generalized kinetic and potential energies. A simple method is introduced for investigating the important issue of handling momentum conservation at the interaction vertices. It is shown that the irrelevance of momentum conservation found by Metzner and Vollhardt applies more generally than their Gaussian density of states. Interactions between particles on different sites are shown to simplify to their Hartree substitute. This leaves on-site interactions as the only dynamical interactions in the limit of infinite dimension.

The Hubbard model at high dimensions: some exact results and weak coupling theory

Recently it was shown that the theory of systems of correlated fermions on a lattice is greatly simplified in the limit of high dimensions as compared to lattice systems of dimensions 2 or 3 or to isotropic systems. We discuss here the implications of the limit of high dimensions on the single particle propagator of the Hubbard model. It is shown that all the typical Fermi liquid features are retained at high dimensions. Some exact results are obtained for infinite dimension: the shape of the Fermi surface as well as the density of states at the Fermi surface are not renormalized at all by the Coulomb interaction as long as the symmetry of the system is not broken. The self-consistent weak coupling theory is cast into a form which is solved numerically with very little effort.

Interface free energy and transition temperature of the square-lattice Ising antiferromagnet at finite magnetic field

We use a simple method to calculate interface properties of the square-lattice Ising antiferromagnet with nearest neighbour interaction. The method bypasses the more complicated bulk problem by taking into account only interface configurations of spins and allows the inclusion of a finite magnetic field. From this we derive two new results: 1) the interface free energy associated with the coexistence of the two antiferromagnetic phases at finite magnetic field, and 2) the transition temperature as a function of the magnetic field which determines the phase boundary.

Self-consistent perturbation theory of the anderson model: Ground state properties

The zero temperature limit of the self-consistent perturbation theory of a degenerate Anderson impurityin a metal is partially solved with analytical methods. In particular, the energy scales relevant to the system are made explicit and closed expressions are derived for the local level propagator around the Fermi energy and for the dynamical susceptibility. Results are compared with what is known from Fermi liquid theory. The argument that the theory is valid for large degeneracy is disturbed by certain pathologies.

Crystal and magnetic structure of LaTiO 3 : Evidence for nondegenerate t 2 g orbitals

The crystal and magnetic structures of LaTiO 3 have been studied by x-ray and neutron-diffraction techniques using nearly stoichiometric samples. We find a strong structural anomaly near the antiferromagnetic ordering T N = 146 K. In addition, the octahedra in LaTiO 3 exhibit an intrinsic distortion, which implies a splitting of the t 2 g levels. Our results indicate that LaTiO 3 should be considered as a Jahn-Teller system where the structural distortion and the resulting level splitting are enhanced by the magnetic ordering.

Dispersion and symmetry of bound states in the shastry-sutherland model

Bound states made from two triplet excitations on the Shastry-Sutherland lattice are investigated. Based on the perturbative unitary transformation by flow equations quantitative properties like dispersions and qualitative properties like symmetries are determined. The high order results [up to (J2/J1)(14)] permit one to fix the parameters of SrCu2(BO3)(2) precisely: J1 = 6.16(10) meV, x J2/J1 = 0.603(3), J( perpendicular) = 1.3(2) meV. At the border of the magnetic Brillouin zone a general double degeneracy is derived. An unexpected instability in the triplet channel at x = 0.63 indicates a transition towards another phase. The possible nature of this phase is discussed.

Magnetic and non-magnetic ground states of the Kondo lattice

We use the variational method to investigate the ground state phase diagram of the Kondo lattice Hamiltonian for arbitraryJ/W, and conduction electron concentrationnc (J is the Kondo coupling andW the bandwidth). We are particularly interested in the question under which circumstances the globally singlet (collective Kondo) Fermi liquid type ground state becomes unstable against magnetic ordering. For the collective Kondo singlet we use the lattice generalization of Yosidas wavefunction which implies the existence of a large Fermi volume, in accordance with Luttingers theorem. Using the Gutzwiller approximation, we derive closed-form results for the ground state energy at arbitraryJ/W andnc, and for the Kondo gap atnc=1. We introduce simple trial states to describe ferromagnetic, antiferromagnetic, and spiral ordering in the small-J (RKKY) regime, and Nagaoka type ferromagnetism at largeJ/W. We study three particular cases: a band with a constant density of states, and the (tight binding) linear chain, and square lattice periodic Kondo models. We find that the lattice enhancement of the Kondo effect, which is described in our theory of the Fermi liquid state, pushes the RKKY-to-nonmagnetic phase boundary to much smaller values ofJ/W than it was previously thought. In our study of the square lattice case, we also find a region of itinerant, Nagaoka-type ferromagnetism at largeJ/W fornc ≦1/3.

Competing non-heisenberg interactions in EuxSr1−xS

Abstract The Curie—Weiss temperature θ 1 ( x ) of the linear susceptibility χ 1 of the diamagnetically diluted ferromagnetic composition series Eu x Sr 1− x S shows a pronounced x 2 term. In contrast to an earlier interpretation this term is explained here by ferromagnetic three-spin interactions which exist in addition to biquadratic and bilinear exchange interactions. Biquadratic and three-spin interactions have been identified by means of the Curie—Weiss temperature θ 3 ( x ) of the cubic susceptibility χ 3 . θ 3 ( x ) contains one negative term proportional to x which is caused by antiferromagnetic biquadratic interactions and one positive term proportional to x 2 attributed to ferromagnetic three-spin interactions. Comparison with the theoretical expressions for θ 1 and θ 3 reveals an excellent consistency of this interpretation and confirms that the x 2 term in θ 3 ( x )) and θ 1 ( x ) is due to ferromagnetic three-spin interactions. These interactions compete with antiferromagnetic biquadratic interactions as it was found in Eu x Sr 1− x Te.

LATTICE DEPENDENCE OF SATURATED FERROMAGNETISM IN THE HUBBARD MODEL

We investigate the instability of the saturated ferromagnetic ground state (Nagaoka state) in the Hubbard model on various lattices in dimensions d=2 and d=3. A variational resolvent approach is developed for the Nagaoka instability both for U = infinity and for U < infinity which can easily be evaluated in the thermodynamic limit on all common lattices. Our results significantly improve former variational bounds for a possible Nagaoka regime in the ground state phase diagram of the Hubbard model. We show that a pronounced particle-hole asymmetry in the density of states and a diverging density of states at the lower band edge are the most important features in order to stabilize Nagaoka ferromagnetism, particularly in the low density limit.

Ferromagnetism in Hubbard models: Low density route

Thirty years ago the Hubbard model was introduced by Gutzwiller, Hubbard and Kanamori with the main purpose of mimicking the ferromagnetism of transition metals. Soon after, Nagaoka and Thouless pointed out a basic mechanism for ferromagnetism in strongly correlated electron systems by studying the motion of a single hole in a half-filled Hubbard model. This important work was hoped to shed light onto metallic ferromagnetism from the low doping regime. Unfortunately, this low doping route towards ferromagnetism has not been successful as far as rigorous results for finite doping concentrations are concerned. In the work presented here, we start from the opposite limit of low particle concentrations. In this limit we provide the first proof of a fully polarized metallic ground state for a Hubbard model. The proof proceeds by mapping Hubbard “zigzag” chains onto a continuum model with an additional degree of freedom and local first Hunds rule coupling. For this model the maximum total spin multiplet is shown to be the unique ground state for infinite Hubbard coupling. Our proof may open a low density route towards the understanding of the ferromagnetism of Hubbard models.