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.
Explicitly given, exact, ground-state solutions are reported for the one-dimensional periodic Anderson model in the limit of strong on-site repulsion, at and above half-filling, in the generic case of the model, for which f-electron hopping is forbidden. The description is presented for Bravais lattices, and the deduction procedure is based on decomposition of the starting Hamiltonian in positive semidefinite operators, which are defined as combinations of fermionic operators acting on the lattice sites of blocks. In comparison with the previously used procedures of this type, we use blocks greater than a unit cell, and a nonlinear combination of fermionic operators acting on the lattice sites. Based on such block operators, the previously known exact, ground-state solution possibilities at one-quarter and three-quarter filling have been extended to half-filling. The deduced ground state is present in restricted regions of the T = 0 phase diagram of the model, and is a spin-singlet conducting state.
Presenting exact solutions for the two-dimensional periodic Anderson model with finite and nonzero on-site interactions
U>0, we describe a rigorous non-Fermi-liquid phase in normal phase and two dimensions. This new state emerges in multiband interacting Fermi systems above half filling, being generated by a flat-band effect. The momentum distribution function ${n}_{\stackrel{\ensuremath{\rightarrow}}{k}}$ 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 $\stackrel{\ensuremath{\rightarrow}}{k}$ space is missing. The state emerges in the vicinity of a Mott insulating phase when lattice distortions are present and is highly degenerated and paramagnetic. A gap is present at high U in the density of low-lying excitations. During low-lying excitations, quasiparticles are not created above the Fermi level, only the number of particles at
eF increases.
We have used the density-matrix renormalization group method to study the ground-state properties of the symmetric periodic Anderson model in one dimension. We have considered lattices with up to
Ns=50 sites, and electron densities ranging from quarter to half filling. Through the calculation of energies, correlation functions, and their structure factors, together with careful extrapolations (toward ${N}_{s}\ensuremath{\rightarrow}\ensuremath{\infty}$), we were able to map out a phase diagram
Uvsn, where
U is the electronic repulsion on
f orbitals, and
n is the electronic density, for a fixed value of the hybridization. At quarter filling,
n=1, our data is consistent with a transition at ${U}_{{c}_{1}}\ensuremath{\simeq}2$, between a paramagnetic (PM) metal and a spin-density-wave (SDW) insulator; overall, the region $U\ensuremath{\lesssim}2$ corresponds to a PM metal for all
n<2. For $1<n\ensuremath{\lesssim}1.5$ a ferromagnetic phase is present within a range of
U, while for $1.5\ensuremath{\lesssim}n<2$, we find an incommensurate SDW phase; above a certain
Uc(n), the system displays a Ruderman-Kittel-Kasuya-Yosida behavior, in which the magnetic wave vector is determined by the occupation of the conduction band. At half filling, the system is an insulating spin liquid, but with a crossover between weak and strong magnetic correlations.
We investigate an extended version of the periodic Anderson model (the so-called periodic Anderson-Hubbard model) with the aim to understand the role of interaction between conduction electrons in the formation of the heavy-fermion and mixed-valence states. Two methods are used: (i) variational calculation with the Gutzwiller wave function optimizing numerically the ground-state energy and (ii) exact diagonalization of the Hamiltonian for short chains. The
f-level occupancy and the renormalization factor of the quasiparticles are calculated as a function of the energy of the
f orbital for a wide range of the interaction parameters. The results obtained by the two methods are in reasonably good agreement for the periodic Anderson model. The agreement is maintained even when the interaction between band electrons,
Ud, is taken into account, except for the half-filled case. This discrepancy can be explained by the difference between the physics of the one- and higher-dimensional models. We find that this interaction shifts and widens the energy range of the bare
f level, where heavy-fermion behavior can be observed. For large-enough
Ud this range may lie even above the bare conduction band. The Gutzwiller method indicates a robust transition from Kondo insulator to Mott insulator in the half-filled model, while
Ud enhances the quasiparticle mass when the filling is close to half filling.