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Philosophical Magazine B

Exact results for the one-dimensional periodic Anderson model at finite U

Iván Orlik, Zsolt Gulácsi

Published Oct 1, 2001• 18 citations
Publisher

Abstract

We present exact results for the periodic Anderson model for finite Hubbard interaction 0 < U < on certain restricted domains of the model's phase diagram, in d = 1 dimension. Decomposing the Hamiltonian into positive semidefinite terms we find two auantum states to be ground states; a completely localized ground state and a non-localized ground state. The ground-state energy and several ground-state expectation values were calculated.

DOI
10.1080/13642810110043240

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Exact results for the one-dimensional periodic Anderson model at finite U

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We present exact results for the periodic Anderson model for finite Hubbard interaction 0 < U < on certain restricted domains of the model's phase diagram, in d = 1 dimension. Decomposing the Hamiltonian into positive semidefinite terms we find two auantum states to be ground states; a completely localized ground state and a non-localized ground state. The ground-state energy and several ground-state expectation values were calculated.
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.
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.
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.