The Summarization Of YBE Theory

Yang Baxter Equation is a powerful tool to handle a large class of nonlinearintegrable systems. In recent years, the research is more extensive. In this paper, thereview of the theory related to the Yang Baxter Equation. First, we reviewed theequation itself, the physical meaning of R-matrix, the RTT relations and the YangBaxteration, which is the basis of this article. Then we introduced the hamiltonianand transition operator, Hamiltonian generated from the R and T, J operator acts as atransition operator and transition operator realization of the hydrogen atoms, theseare formed theory, those can help us understanding the Yang Baxter Equation andyangian algebra. Finally, the R-matrix, operator J in the application of the geometricphase and entanglement. Phase and entanglement is the cutting-edge issues ofquantum mechanics, their research seems necessary. In this paper, as a simpleexample illustrates the R, J the role and influence of the berry phase andentanglement. Specifically, we compared the entanglement of the spin1/2particle ina constant magnetic field with or without the J operater. The entanglement varieswith time and size is adjustable with the influence of J.There are many theory related to the Yang Baxter Equation, for example, it canuse in high energy physics. This is still the subject of efforts and the focus of futureefforts. I hope in the near future, similar overview will be content in this area.