The Application Of Yang-Baxter System In Quantum Physics

Recently, Yang-Baxter Equation and its theories have made great progress in the applications of quantum physics. In this paper, we mainly introduce its applications of the thermal entanglement, the ESD and the Berry phase.Firstly,Yang-Baxter system is applied to the Berry phase. In this paper, we introduce the braiding matrix, then by the trigonometric Yang-Baxterization approach, we can get the unitary Yang-Baxter R? -matrix base on which the Hamitionian H (θ,φ) can be constructed. Hereafter, through simplifying the Hamitionian, we solve its eigenstates which we substitute into Berry phase formula so that we can obtain the Berry phase in the Hamiltionian system and quantum critility phenomenon is also discussed.Secondly, Yang-Baxter system is applied to the thermal entangement and the entanglement sudden death. A series of studies have shown that YEB has a deep connection with quantum computation and entanglement swapping. In this paper, by Yang-Baxterization approach, we can obtain a unitary solution R? (θ,φ) which we use to construct the new Hamiltonians. Then we solve the eigen-problem of the Hamiltionia H (θ,φ) so that we can derive density matrix that we substitute into the definition of concurrence in order to get the degree of entanglement, and then we can investigate the thermal entanglement and the ESD by discussing the changes of concurrence as its parameters change. In addition, here we choose the unitary Yang-Baxter matrix as the unitary transformational matrix, because the states have the same degree of entanglement when the unitary Yang-Baxter matrix acts on direct-product states.By introducing the Yang-Baxter system in the application of the above three aspects, we can see the feasibility and the practicality of solving the quantum physics problems with the Yang-Baxter theories, which can encourage us to explore its greater potential for applications and solve more physics problem.