Bethe-ansatz, Yang-Baxter equation and factorization of S-matrix.

Eugène Gutkin

C. Destri, Hector J. de Vega

Vahid Karimipour

Within the Matrix Product Formalism we have already introduced a multi-species exclusion process ( Phys. Rev. E , 59 (1999) 25, cond-mat/9809193), in which different particles hop with different rates and fast particles stochastically overtake slow ones. In this letter we show that on an open chain, the master equation of this process can be exactly solved via the coordinate Bethe ansatz. It is shown that the N -body S -matrix of this process is factorized into a product of two-body S -matrices, which in turn satisfy the quantum Yang-Baxter equation (QYBE). This solution is, to our knowledge, a new solution of QYBE.

Mo‐Lin Ge, Kang Xue

Jeffrey Robert Schmidt

The algebraic Bethe Ansatz is carried out for models (dimer models on a hexagonal lattice) whose matrix of local Boltzmann weights fails to satisfy the Yang–Baxter equation. The operator algebra is constructed instead by a generalizable alternative process using only the coproduct decomposition of the operators. The new technique makes it possible to solve many lattice N-body models whose local Boltzmann weights fail to meet the algebraic requirements of the Yang–Baxter equation.PACS Nos.: 02.20.Uw, 24.10.Cn, 87.10.Hk, 05.20.–y

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.