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arXiv:cond-mat/0504174 · Physical Review B

Exact ground states of the periodic Anderson model in D=3 dimensions

Zsolt Gulácsi, D. Vollhardt

Published Aug 23, 2005• 31 citations
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Abstract

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.

DOI
10.1103/physrevb.72.075130

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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.
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.
The derivation procedure of exact ground states for the periodic Anderson model (PAM) in restricted regions of the parameter space and D=2D=2D=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.
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.
Presenting exact solutions for the two-dimensional periodic Anderson model with finite and nonzero on-site interactions U>0,U>0,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),{(e}_{F}),(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{e}_{F}eF​ increases.