Zsolt Gulacsi

Exact many-electron ground states on the diamond Hubbard chain.

Exact ground states of interacting electrons on the diamond Hubbard chain in a magnetic field are constructed which exhibit a wide range of properties such as flat-band ferromagnetism and correlation-induced metallic, half-metallic, or insulating behavior. The properties of these ground states can be tuned by changing the magnetic flux, local potentials, or electron density.

Exact insulating and conducting ground states of a periodic Anderson model in three dimensions.

We present a class of exact ground states of a three-dimensional periodic Anderson model at 3/4 filling. Hopping and hybridization of d and f electrons extend over the unit cell of a general Bravais lattice. Employing novel composite operators combined with 55 matching conditions the Hamiltonian is cast into positive semidefinite form. A product wave function in position space allows one to identify stability regions of an insulating and a conducting ground state. The metallic phase is a non-Fermi liquid with one dispersing and one flat band.

Theory of phase transitions in two-dimensional systems

A detailed description of phase transitions in two dimensions is presented based on the two-dimensional classical XY model. After describing the basic physics of topological ordering, the starting model Hamiltonian is constructed for a detailed study. Following this, a direct space renormalization programme is presented. The obtained phase transition is analysed in detail based on the scaling equations. The systematic renormalization group calculation up to third order based on field-theoretical techniques is also presented. The notion of topological excitations from the viewpoint of the dual model is analysed in detail. The D > 2 cases are analysed through the three-dimensional XY model and layered systems. This article is pedagogical in nature and is intended to be accessible to any graduate student or physicist who is not an expert in this field.

Route to Ferromagnetism in Organic Polymers

Employing a rigorous theoretical method for the construction of exact many-electron ground states we prove that interactions can be employed to tune a bare dispersive band structure such that it develops a flat band. Thereby, we show that pentagon-chain polymers with electron densities above half filling may be designed to become ferromagnetic or half metallic.

Exact solutions for the periodic Anderson model in two dimensions: A non-fermi-liquid state in the normal phase

Presenting exact solutions for the two dimensional periodic Anderson model with finite and nonzero on-site interaction U > 0, we are describing a rigorous non-Fermi liquid phase in normal phase and 2D. This new state emerges in multi-band interacting Fermi systems above half filling, being generated by a flat band effect. The momentum distribution function n~k together with its derivatives of any order is continuous. The state possesses a well defined Fermi energy (eF), but the Fermi momentum concept is not definable, so the Fermi surface in ~ k-space is missing. The state emerges in the vicinity of a Mott insulating phase when lattice distortions are present, is highly degenerated and paramagnetic. A gap is present at high U in the density of low lying excitations. During low lying excitations, quasi-particles are not created above the Fermi level, only the number of particles at eF increases.

Exact Stripe, Checkerboard and Droplet Ground States in Two Dimensions

Exact static nondegenerate stripe and checkerboard ground states are obtained in a two-dimensional generalized periodic Anderson model, for a broad concentration range below quarter filling. The random droplet states, also present in the degenerate ground state, are eliminated by extending the Hamiltonian with terms of different physical origin such as dimerization, periodic charge displacements, density waves, or distortion lines.

Exact Many-Electron Ground States on Diamond and Triangle Hubbard Chains

We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground state of this Hamiltonian, and (iii) the proof of the uniqueness of the ground state. This approach works in any dimension, requires no integrability of the model, and only demands sufficiently many microscopic parameters in the Hamiltonian which have to fulfill certain relations. The scheme is first employed to construct exact ground state for the diamond Hubbard chain in a magnetic field. These ground states are found to exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior, which can be tuned by changing the magnetic flux, local potentials, or electron density. Detailed proofs of the uniqueness of the ground states are presented. By the same technique exact ground states are constructed for triangle Hubbard chains and a one-dimensional periodic Anderson model with nearest-neighbor hybridization. They permit direct comparison with results obtained by variational techniques for f -electron ferromagnetism due to a flat band in CeRh3B2.

Exact results for the one-dimensional periodic Anderson model at finite U

Abstract We present exact results for the periodic Anderson model for finite Hubbard interaction 0 < U < on certain restricted domains of the models phase diagram, in d = 1 dimension. Decomposing the Hamiltonian into positive semidefinite terms we find two auantum states to be ground states; a completely localized ground state and a non-localized ground state. The ground-state energy and several ground-state expectation values were calculated.

Delocalization effect of the Hubbard repulsion in exact terms and two dimensions.

The genuine physical reasons explaining the delocalization effect of the Hubbard repulsion U are analyzed. First it is shown that always when this effect is observed, U acts on the background of a macroscopic degeneracy present in a multiband type of system. After this step I demonstrate that acting in such conditions, by strongly diminishing the double occupancy, U spreads out the contributions in the ground state wave function, hence strongly increases the one-particle localization length, consequently extends the one-particle behavior producing conditions for a delocalization effect. To be valuable, the reported results are presented in exact terms, being based on the first exact ground states deduced at half filling in two dimensions for a prototype two band system, the generic periodic Anderson model at finite value of the interaction.

Exact Ground States of the Periodic Anderson Model in D = 3 Dimensions

We construct a class of exact ground states of three-dimensional periodic Anderson models (PAMs) — including the conventional PAM — on regular Bravais lattices at and above 3/4 filling, and discuss their physical properties. In general, the f electrons can have a (weak) dispersion, and the hopping and the non-local hybridization of the d and f electrons extend over the unit cell. The construction is performed in two steps. First the Hamiltonian is cast into positive semi-definite form using composite operators in combination with coupled non-linear matching conditions. This may be achieved in several ways, thus leading to solutions in different regions of the phase diagram. In a second step, a non-local product wave function in position space is constructed which allows one to identify various stability regions corresponding to insulating and conducting states. The compressibility of the insulating state is shown to diverge at the boundary of its stability regime. The metallic phase is a non-Fermi liquid with one dispersing and one flat band. This state is also an exact ground state of the conventional PAM and has the following properties: (i) it is nonmagnetic with spin-spin correlations disappearing in the thermodynamic limit, (ii) density-density correlations are short-ranged, and (iii) the momentum distributions of the interacting electrons are analytic functions, i.e., have no discontinuities even in their derivatives. The stability regions of the ground states extend through a large region of parameter space, e.g., from weak to strong on-site interaction U. Exact itinerant, ferromagnetic ground states are found at and below 1/4 filling.