Algebraic Bethe ansatz

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.

Fabio Franchini

Frank Göhmann, Er Seel, Fachbereich Physik

We solve the gl(1|2) generalized model by means of the algebraic Bethe ansatz. The resulting eigenvalue of the transfer matrix and the Bethe ansatz equations depend on three complex functions, called the parameters of the generalized model. Specifying the parameters appropriately, we obtain the Bethe ansatz equations of the supersymmetric t-J model, the Hubbard model, or of Yang’s model of electrons with delta interaction. This means that the Bethe ansatz equations of these (and many other) models can be obtained from a common algebraic source, namely from the Yang-Baxter algebra generated by the gl(1|2) invariant R-matrix.

Č. Burdík, Ondřej Navrátil

We show how to formulate the algebraic nested Bethe ansatz for RTT algebras with an R-matrix of the sp( 4 ) type. We obtain the Bethe vectors and Bethe conditions for any highest-weight representation of these RTT algebras.