The derivation procedure of exact ground states for the periodic Anderson model (PAM) in restricted regions of the parameter space and
D=2 dimensions using plaquette operators is presented in detail. Using this procedure, we are reporting exact ground states for PAM in two dimensions and finite value of the interaction, whose presence do not require the next-to-nearest-neighbor extension terms in the Hamiltonian. In order to do this, a completely new type of plaquette operator is introduced for PAM, based on which a localized phase is deduced whose physical properties are analyzed in detail. The obtained results provide exact theoretical data that can be used for the understanding of system properties leading to metal-insulator transitions, strongly debated in recent publications in the frame of PAM. In the described case, the loss of the localization character is connected to the breakdown of the long-range density-density correlations rather than Kondo physics.
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.