WFU Physics Colloquium

TITLE: Electron-electron interactions in solids: analytic results for the Hubbard model in the atomic limit

SPEAKER: William B. Hodge,

TIME: Thursday Apr. 17, 2008 at 4:00 PM

PLACE: Room 101 in Olin Physical Laboratory

In 1963 J. Hubbard introduced a model to describe electron interactions in solids; 45 years later, there are still some disagreements about the properties of this model, and it is still actively studied. Though it describes a very simplified view of solids, it is surprisingly complex and capable of qualitatively describing many phenomena not possible in band theory alone, such as magnetic ordering and Mott metal-insulator transitions. After a brief overview of the model, we will focus on the case of finite Hubbard rings in the atomic limit. We will critically examine and then propose a correct solution to the simple, but historically important, problem of ferromagnetism with one hole, initially studied by Nagaoka. From there, we will use the Bethe ansatz technique to obtain an expression for the ground state energy of a system with arbitrary filling. Our findings are in disagreement with some previous published results but agree with results obtained by our exact diagonalization.