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.
The ground-state energy, wave-function, hybridization gap and magnetic phasediagram of the Single Site Impurity Anderson Model (SIAM) and the Periodic AndersonModel (PAM) were calculated using Exact-Diagonalization (ED) technique. The EDtechnique was applied to the SIAM and PAM in one dimension before speculating on Ce 4fbeing a test bed of the results, since it has 4f localized electrons in the Heavy fermioncompound CeCu2Si2. Each of the results obtained describe the evolution of the electronicsystem in terms of a simple set of parameters.The parameter regimes studied suggest asmooth phase transition from an antiferromagnetic (AFM) phase to a ferromagnetic (FM)phase at quarter fillings in one dimension when t increases and a magnetic instability wasobserved as U → ∞. The role of hybridization between the conduction electrons and thelocalized f orbital in the Anderson impurity in a semiconductor was also investigated as Vincreases in the SIAM and the PAM.
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.
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 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.