Third Component Open Model The Exact Solution Of The Boundary Bariev

Bariev model is one of the most significant models in condensed matter physics, which is relevant to the high- T_c superconductivity. It has been extensively studied in the periodiccase, its exact solution in one-dimension can be obtained through Bethe ansatz method. Although there are a few works have been done about the solution of two- and three-component open Bariev models, the solution of three-component Bariev model under open boundary conditions has not been given though the algebraic Bethe ansatz method. Furthermore, the boundary effect is also an important topic in condensed matter physics, which is closely related to find the exact solution with open boundaries in one-dimension. Thus it is an interesting work to study the three-component Bariev model under open boundary conditions by the algebraic Bethe ansatz method.In this dissertation, we construct the Bariev model with nine kinds of boundary fields by the matrices K_± defining the boundaries. And then the Lax operator is given in the form ofmatrix, as well as the basic quantities, e.g., the R -matrix, the monodromy matrices and the transfer matrices are defined. By using the expression of the local Lax operator of the model,the action of the monodromy matrices T, T^-1, U on the pseudo-vacuum state is given outin detail. Furthermore, the main fundamental commutation relations are obtained through the reflection equations, the recursive n-particle state as well as the one-particle exact solution is given and the Bethe ansatz equations are found accordingly. Finally, we list the nesting boundary K matrices, which play a crucial role for obtaining the n-particle solution and finding the Bethe ansatz equations, the eigenvalues of the transfer matrices and the energy spectrum of the system by means of the nested algebraic Bethe ansatz method.