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Physical Review Letters

Exact ground-state energy of the periodic Anderson model ind=1 and extended Emery models ind=1,2 for special parameter values

Rainer Strack

Published Feb 8, 1993• 46 citations
Publisher

Abstract

We generalize an approach, which was recently introduced by Brandt and Giesekus to calculate the exact ground-state energy for strongly interacting particles on special perovskitelike lattices, to the periodic Anderson model in the dimension d=1 and to extended Emery models in d=1,2 on regular lattices for arbitrary spin degeneracy. For these models we calculate the exact ground-state energy for a restricted parameter regime in the strong-coupling limit. The ground-state energy shows a simple algebraic structure. We also present an eigenfunction of the Hamiltonian with the ground-state energy as its corresponding eigenvalue.

DOI
10.1103/physrevlett.70.833

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We generalize an approach, which was recently introduced by Brandt and Giesekus to calculate the exact ground-state energy for strongly interacting particles on special perovskitelike lattices, to the periodic Anderson model in the dimension d=1 and to extended Emery models in d=1,2 on regular lattices for arbitrary spin degeneracy. For these models we calculate the exact ground-state energy for a restricted parameter regime in the strong-coupling limit. The ground-state energy shows a simple algebraic structure. We also present an eigenfunction of the Hamiltonian with the ground-state energy as its corresponding eigenvalue.
We study the exactly solvable strongly interacting electron models recently introduced by Brandt and Giesekus and further generalized by other authors. For a very general class of models, including the Hubbard, the periodic Anderson, and the Emery models with certain hopping matrices and infinitely large on-site Coulomb repulsion on d sites, we prove that the known exact ground state is indeed the unique ground state for a certain electron number. The uniqueness guarantees that one can discuss physics of various strongly interacting electron systems by analyzing the exact ground states.
Exact solutions of the Hubbard model and the periodic Anderson model in the limit of infinite interaction strength are presented. Both models are studied on a D-dimensional decorated hypercubic lattice with periodic boundary conditions for any dimension D\ensuremath{\ge}2 and arbitrary size. The lattice is very similar to the perovskite lattice. In addition to the ground-state energy, a corresponding eigenstate is constructed. This ground state contains at least two particles per unit cell. For the Anderson model, the exact solution is restricted to a surface in the (Ef{\mathit{E}}_{\mathit{f}}Ef​,V) parameter space; however, the resulting relation V(Ef{\mathit{E}}_{\mathit{f}}Ef​) does not lead to unphysical parameters.
We present exact results for the extended periodic Anderson model with Falicov-Kimball interactions in one dimension (d=1).(d=1).(d=1). Ground-state energies and their corresponding wave functions are obtained for a restricted region of the parameter space of the model Hamiltonian. In particular, two ground states are obtained, one containing one electron per site and the other three electrons per site. The expectation values of the occupation numbers and of the excitonic correlation functions 〈cf+〉〈{\mathrm{cf}}^{+}〉〈cf+〉 are calculated using the exact ground state wave functions. Finally we discuss the possibility of a ferroelectric ground state in the Falicov-Kimball model.