Integrable one-dimensional heavy fermion lattice model

Andrei A. Zvyagin, P. Schlottmann

We consider a one-dimensional supersymmetric t−J model and introduce a finite concentration of impurities of arbitrary spin S without destroying the integrability. Using the Bethe ansatz equations diagonalizing the correlated host with impurities, we discuss the ground state properties as a function of magnetic field H and the Kondo exchange coupling. While an isolated impurity of spin S>1/2 has a magnetic ground state of effective spin (S−12), a finite concentration introduces a heavy impurity band and yields a singlet ground state with antiferromagnetically correlated impurities. A field H first polarizes the narrow impurity band. The impurities have mixed valent properties induced in part by correlations in the host. Some aspects of the model are related to heavy fermion alloys.

Shuichi Murakami

Okunzuwa I. Samuel, C. Okaro Augustine

The Kondo interaction coupling, Heisenberg exchange coupling, and Coulomb interactions within d-sites, were introduced in a one dimensional Periodic Anderson Model Hamiltonian (PAMH) to further investigate the effects of interaction parameters on the ground state energy of systems with heavy fermions (HF) behavior. Periodic Anderson model PAM being one of the most successful model for studying the heavy fermions System (HFS) was used in an extended version (mixed Kondo-Anderson representation) on a system of three-electrons interacting on three-sites cluster. Exact Diagonalization technique (EDT) normally used to solve conventional PAM calculation was considered in this work for a very small cluster. Hamiltonian used to describe this model contains the usual term describing the kinetic energy of the system, on-site coulomb repulsion and a hopping integral. The Hamiltonian is acted on the different Hilbert states of the lattice system and results of the interactions were obtained in terms of hopping integral, coulomb repulsions, exchange couplings and the hybridization term. Graphs of ground state energy Eo plotted agains tthese interaction parameters were presented in a clear format. As these parameters were varied numerically through a finite range of values, the individual effects of these parameters on the system’s ground state energy were observed and discussed. Hence, the results obtained from this work shows theoretically how the tuning of the Columbic interaction within the conduction band provides information that sheds light on the underlying physics of the heavy fermions systems models. Results obtained from this work further demonstrate the reliability of the model Hamiltonians that we have harnessed and the importance of considering electron-lattice interactions as well as interactions that account for magnetic impurities for the proper description of heavy fermions material.

E. M�ller-Hartmann

Joe Mitchell, Tigran Sedrakyan, Victor M. Galitski

P. Schlottmann

A lattice model consisting of a single narrow band is introduced to describe some aspects of heavy electrons. The model excludes double occupancy of the sites and electrons on nearest-neighbor sites interact via a charge interaction and spin exchange. The model is integrable in one dimension for some special values of the coupling constants. These cases are related to the SU(3) invariance. The Bethe-ansatz equations are obtained and ground-state and thermodynamic properties are discussed and solved in some limiting cases.