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.
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 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.
Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matrix embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin–spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin–spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.
We have studied the ground-state properties of the symmetric and asymmetric one-dimensional periodic Anderson model as a function of band filling and the model parameters
(V,U,and
Ef) using the local mean-field (LMF) approach. We have constructed the phase diagram for both cases and have calculated the energy, local moment, and occupation number of the f level. The LMF approach can reveal the basic properties of the system throughout the entire parameter space. For the symmetric case ${(E}_{f}=\ensuremath{-}U/2),$ close to quarter and half filling the antiferromagnetic phase is the ground state. For intermediate band-filling there is a second-order phase transition to a ferromagnetic state. At quarter filling there is a transition from a metallic paramagnetic state to an insulating antiferromagnetic state as the on-site Coulomb interaction increases. The asymmetric case is treated in the mixed-valence regime
(Ef=0). At half filling the ground state is antiferromagnetic while at or close to quarter filling it is paramagnetic. Below half filling the ground state becomes ferromagnetic, suggesting that doping destroys rapidly the antiferromagnetic $f\ensuremath{-}f$ spin correlations. For small values of U we find a paramagnetic state at all band fillings. Results for the average occupation number of the f level compare well with density matrix renormalization group calculations.
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.