Thermodynamic Limits And Boundary Energy Of The Integrable Models Without U(1) Symmetry

The integrable models play important roles in quantum field theory,condensed matter physics and statistical physics,which provides solid benchmarks for many important physical problems.The integrable models with U(1)symmetry breaking widely exist in physics,such as the systems with particle unconservation,the systems with unparallel boundary fields,the systems with twisted boundary condition,etc.Recently,a large class of integrable models without U(1)symmetry has been exactly solved to make the study of integrable models is one of the hot spots in the current field of mathematical physics.The method to solve the models proposed by Wang and Yang's group and be called off-diagonal Bethe ans(?)tze method.Based on the exact solution,the thermodynamic limit and boundary energy of the models have attracted great attention.Besides,based on the relation between the spin chain model and the asymmetric simple exclusion process,we give the exact solution of the asymmetric simple exclusion process with arbitrary boundary conditions.The objects of this dissertation mainly includes the spin chains and the supersymmetric t-J model in condensed matter physics and the asymmetric simple exclusion process in the non-equilibrium statistical physics.By analytical calculation and numerical simulation,we obtain the thermodynamic limit and boundary energy of the spin-1/2 XXX chain with arbitrary boundary fields.The research provides a new idea for similar problems.The basic idea of the thermodynamic analysis of the integrable models without U(1)symmetry is as followings: the first step is to wipe out the inhomogeneous term in the inhomogeneous T-Q relations directly;The second step is to analyze the contribution of the inhomogeneous term to the ground state energy by numerical calculation.If the contribution of the inhomogeneous term tends to 0 when the size of the system tends to infinity,it is reasonable to conclude that the inhomogeneous term in the inhomogeneous T-Q relation can be ignored during the thermodynamic limit;In the third step,the thermodynamic limit can be obtained by using the thermodynamic Bethe ans(?)tze method,and the boundary properties of the system,such as boundary energy,can be analyzed.Furthermore,the thermodynamic limit and boundary energy of the spin-1 XXX chain with non-diagonal boundary fields are studied.With the same process,we obtain the thermodynamic limit and boundary energy of the supersymmetry t-J model.Asymmetric simple exclusion process is an integrable model in non-equilibrium statistical physics.Although the model is simple,it has many complex phenomena such as boundary induced phase transitions and spontaneous symmetry breaking.The model has two special cases:totally asymmetric simple exclusion process and symmetric simple exclusion process.When the boundary parameters satisfies certain conditions,the exact solution of these models can be obtained by DEHP method.We introduce the DEHP method by taking the total asymmetric simple exclusion process as an concrete example.For the asymmetric simple exclusion process with arbitrary boundaries and it's two special cases,we use the off-diagonal Bethe ans(?)tze method to give their exact solutions.