We investigate Gutzwiller-correlated wave functions as variational ground states for the periodic Anderson model. We extend a recently developed technique for the Hubbard model to the case of two hybridized bands with degeneracy N. We calculate expectation values in the following limits: dilute system (single-impurity case), large degeneracy N, and large dimension d. The mean-field results using the slave-boson approach of Coleman and of Kotliar and Ruckenstein are reproduced in the large-N and large-d limit, respectively. These techniques, therefore, obey variational principles at T=0 in the respective limits and their applicability for T>0 is naturally limited to the Fermi-liquid regime. Evaluations of Gutzwiller-correlated wave functions using the ``Gutzwiller approximation'' are seen to become exact in the limit of large dimensions. A systematic expansion in 1/d can be performed for N=2. In general, corrections are small, of order 1/(dN).
A simple variational description is given on the nature of overlapping Kondo clouds, which compensate the localized f-spins in the Kondo lattice. It is shown explicitly that the f-electrons participate in forming a “large Fermi surface”, although they are strictly localized. The resulting correlated Fermi liquid, i.e., heavy fermions, is examined with the variational Monte Carlo method and is compared with the Gutzwiller approximation. The relation to the periodic Anderson model is also discussed in this connection.
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.
Abstract We discuss a variational ground state wave function for the symmetric periodic Anderson model with commensurate spin density order. The energy of this ansatz is evaluated in closed form. Our approach generalizes a variational treatment proposed recently by Strack and Vollhardt and results in significantly lower energy. Contrary to the Gutzwiller ansatz the wave function recovers the Schrieffer‐Wolff limit for large Coulomb repulsion. We clarify the relation of our approach to unrestricted Hartree‐Fock and present a comparison with existing quantum Monte Carlo calculations for one dimension.
The electronic ground states for two- and three-dimensional Anderson-lattice clusters with large Hubbard repulsion are determined variationally within the Gutzwiller ansatz by use of a stochastic algorithm for exact evaluation of matrix elements of Gutzwiller states. The algorithm is similar to one normally used for finite-temperature simulation and is described in some detail. Variational states for a variety of Hamiltonian parameters and particle densities were considered. Of particular interest is the regime of small interband hopping, which is antiferromagnetic at densities near two particles per unit cell. We found that for some Hamiltonian-parameter regimes, doping the antiferromagnetic cluster with enough particles or holes can destroy the magnetic ordering and produce a state that resembles a heavy-Fermi-liquid state, a metal with a strongly-frequency-dependent self-energy. For a 4\ifmmode\times\else\texttimes\fi{}4 Anderson lattice, we present results of low-temperature quantum Monte Carlo simulations to evaluate the validity of the variational Gutzwiller ansatz.
We propose a new variational wave function for the periodic Anderson model in the case of antiferromagnetically ordered f-electrons. Expectation values in terms of this wave function can be calculated analytically in arbitrary dimensions d. The wave function automatically produces the exact limiting behavior of the ground state energy for weak hybridization and strong f-electron interaction in the symmetric case, which the Gutzwiller wave function fails to do. Several additional improvements are discussed. Thereby one obtains a wave function that leads to extremely good ground state energies for the periodic Anderson model for arbitrary U in all dimensions d.