We present exact results for the extended periodic Anderson model with Falicov-Kimball interactions in one dimension $(d=1).$ Ground-state energies and their corresponding wave functions are obtained for a restricted region of the parameter space of the model Hamiltonian. In particular, two ground states are obtained, one containing one electron per site and the other three electrons per site. The expectation values of the occupation numbers and of the excitonic correlation functions $〈{\mathrm{cf}}^{+}〉$ are calculated using the exact ground state wave functions. Finally we discuss the possibility of a ferroelectric ground state in the Falicov-Kimball model.We present exact results for the extended periodic Anderson model with Falicov-Kimball interactions in one dimension $(d=1).$ Ground-state energies and their corresponding wave functions are obtained for a restricted region of the parameter space of the model Hamiltonian. In particular, two ground states are obtained, one containing one electron per site and the other three electrons per site. The expectation values of the occupation numbers and of the excitonic correlation functions $〈{\mathrm{cf}}^{+}〉$ are calculated using the exact ground state wave functions. Finally we discuss the possibility of a ferroelectric ground state in the Falicov-Kimball model.

Physical review. B, Condensed matterJun 20, 200215 citations

Superconducting Ground States in Extended Hubbard Models

Pinaki Sengupta, David K Campbell

APSMar 1, 19960 citations

Exact ground-state energy of the periodic Anderson model ind=1 and extended Emery models ind=1,2 for special parameter values

Rainer Strack

We generalize an approach, which was recently introduced by Brandt and Giesekus to calculate the exact ground-state energy for strongly interacting particles on special perovskitelike lattices, to the periodic Anderson model in the dimension d=1 and to extended Emery models in d=1,2 on regular lattices for arbitrary spin degeneracy. For these models we calculate the exact ground-state energy for a restricted parameter regime in the strong-coupling limit. The ground-state energy shows a simple algebraic structure. We also present an eigenfunction of the Hamiltonian with the ground-state energy as its corresponding eigenvalue.We generalize an approach, which was recently introduced by Brandt and Giesekus to calculate the exact ground-state energy for strongly interacting particles on special perovskitelike lattices, to the periodic Anderson model in the dimension d=1 and to extended Emery models in d=1,2 on regular lattices for arbitrary spin degeneracy. For these models we calculate the exact ground-state energy for a restricted parameter regime in the strong-coupling limit. The ground-state energy shows a simple algebraic structure. We also present an eigenfunction of the Hamiltonian with the ground-state energy as its corresponding eigenvalue.

Physical Review LettersFeb 8, 199346 citations

Perturbation theory for the periodic Anderson model: II. Superconducting state

V. A. Moskalenko

Theoretical and Mathematical PhysicsSep 1, 199810 citations

Superconductivity within the extended Hubbard model

Rene Jursa, S. Wermbter, G. Czycholl

Czechoslovak Journal of PhysicsFeb 1, 19962 citations

Exact ground states of the periodic Anderson model in D=3 dimensions

Zsolt Gulácsi, D. Vollhardt

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 nonlocal 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 semidefinite form using composite operators in combination with coupled nonlinear 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 nonlocal 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.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 nonlocal 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 semidefinite form using composite operators in combination with coupled nonlinear 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 nonlocal 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.

arXiv:cond-mat/0504174Physical Review BAug 23, 200531 citations

We present exact results for the extended periodic Anderson model with Falicov-Kimball interactions in one dimension

(d=1).

Ground-state energies and their corresponding wave functions are obtained for a restricted region of the parameter space of the model Hamiltonian. In particular, two ground states are obtained, one containing one electron per site and the other three electrons per site. The expectation values of the occupation numbers and of the excitonic correlation functions

〈{\mathrm{cf}}^{+}〉

are calculated using the exact ground state wave functions. Finally we discuss the possibility of a ferroelectric ground state in the Falicov-Kimball model.

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 nonlocal 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 semidefinite form using composite operators in combination with coupled nonlinear 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 nonlocal 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.