N-component Open The Exact Solution And Its Thermodynamic Properties Of The Boundary Bariev Model

Multicomponent Bariev model is one of the most significant models in condensed matter physics, which is relevant to the high-Tc superconductivity. It has been extensively studied in the periodic case, its exact solution in one-dimension can be obtained through Bethe ansatz method and some thermodynamics have been calculated such as specific heat and magnetic susceptibility. Although there are a few works about the solution of two- and three-component open Bariev models, the solution and the thermodynamics of the one-dimensional iV-component Bariev's model under open boundary conditions has not been given out yet. On the other hand, the boundary effects 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 such system with non-trivial boundaries.In this dissertation, we first construct the integrable boundary interaction terms in Hamiltonian from the generalized Hamiltonian of the N-component Bariev model under open boundary conditions through the coordinate Bethe ansatz method. During the course, we also derive out the two-particle scattering matrix and the reflecting matrix. Then, we set up the double-row monodromy matrix of the Hamiltonian, the transfer matrix and the reflection equation of the system with the help of the scattering matrix and the reflecting matrix. By expanding the Yang-Baxter relation and the reflection equation, we obtain the commutation relations of the elements of the double-row monodromy matrix. After defining the reference state, we solve the eigenvalue problem of the transfer matrix and give the Bethe ansatz equations and the energy spectrum of the Hamiltonian in the framework of quantum inverse scattering method. We also derive out the thermodynamic Bethe ansatz equations and free energy based on the string hypothesis for both repulsive and attractive interactions. These equations are discussed in some limiting cases, such as the ground state, weak and strong coupling.