Berry Phase Of Heisenberg Models In Bipartite Systems Considered The Yangian Operator

There are lots of integrable models in quantum mechanics,including linear quantum integrable problems and nonlinear quantum integrable problems.To discuss these issues we often cannot proceed without discussion of these models’ symmetry.In the last century sixty or seventy’s C.N. Yang and R.J. Baxter seperately achieved a critical equation which can be applied to the discussion of these symmetry-- Yang Baxter equation.Based on the field,Drinfeld established Yangian.There will be some special changes when the Yangian operator considered for some models.People have achieved great progress in the study on its physical implementation.We know that the various external conditions(including temperature, electric field,magnetic field,impurity and so on) can affect various characteristics of a system including the degree of entanglement,berry phase,etc.So we can adjust these external conditions to achieve our aim.For example,we can adjust the characteristics of the system by means of uniform magnetic field or nonuniform magnetic field,temperature,the amount of impurities.This paper mainly studied the Heisenberg XXX model of two spin 1/2 fermion system.Each of two particles is in a time-dependent rotating magnetic field(the vector has a precessional motion over time),and we also considered a interaction of magnetic field and the Yangian operator.We solved the eigenvalues and eigenvectors by constructing the each element of Hamiltonian operator matrix representation.Then we calculated each instantaneous berry phase of eigenvectors under special conditions and explored the Berry phase of the system under the addition to the Yangian operator.We found that the Berry phase is zero in special situation model after adding Yangian through calculation. This also provides abundant means for various experiments about the physical implementation.The research in experiment on XXX model has been quite mature.We hope that we can verify these through some simple experiments,which is also the purpose and significance of this paper.