Bethe Ansatz

Johnson Leow

In the present thesis, we will review various Bethe ansatz techniques such as the (nested)\nalgebraic Bethe ansatz and the (nested) coordinate Bethe ansatz using well known models\nlike the XXX model and the Hubbard model. Subsequently, the Bethe ansatz techniques\nare applied to obtain Bethe ansatz equations and Bethe vectors of the su(2|2)-invariant S -\nmatrix. Finally, these results are used to obtain the full S -matrix and Bethe equations of the\nstring sigma model.

Bill Sutherland

Hans-Peter Eckle

Abstract The Bethe ansatz can be generalized to problems where particles have internal degrees of freedom. The generalized method can be viewed as two Bethe ansätze executed one after the other: nested Bethe ansatz. Electronic systems are the most relevant examples for condensed matter physics. Prominent electronic many-particle systems in one dimension solvable by a nested Bethe ansatz are the one-dimensional δ-Fermi gas, the one-dimensional Hubbard model, and the Kondo model. The major difference to the Bethe ansatz for one component systems is a second, spin, eigenvalue problem, which has the same form in all cases and is solvable by a second Bethe ansatz, e.g. an algebraic Bethe ansatz. A quantum dot tuned to Kondo resonance and coupled to an isolated metallic ring presents an application of the coupled sets of Bethe ansatz equations of the nested Bethe ansatz.

Evgeny Konstantinovich Sklyanin

Cisar Gómez, Martm Ruiz-Altaba, Germán Sierra

Guang-Liang Li, Kang-Jie Shi

We present a unified algebraic Bethe ansatz for open vertex models which are associated with the non-exceptional A 2 n (2) , A 2 n −1 (2) , B n (1) , C n (1) , D n (1) Lie algebras. Using the algebraic Bethe ansatz, we solve these models with the trivial K -matrix and find that our results agree with that obtained by analytical Bethe ansatz. We also solve the B n (1) , C n (1) , D n (1) models with some non-trivial diagonal K -matrices (one free parameter case) by the algebraic Bethe ansatz.