Taking Into Account The Spin - Orbit Interaction In Solid Squares Point Of The Energy Gap

Strongly-correlated electron systems in the presence of orbital degeneracy have attracted much interest due to experimental advances metal compounds, and the orbital ordering as well as the orbital density wave has been observed in a family of manganites. Among the experimental findings materials are related to spin-orbital systems in one dimension, such as tetrahis (dimethylamino) ethylene-C60, artificial quantum dot arrays, Na2Ti2Sb2O and NaV2O5 degenerate chains, and so forth.The formation of a spin gap in two- or higher dimensional quantum spin systems is a long-standing issue strongly correlated problems. The existence of the gap depends on coupled form of spin angular momentum and orbital angular momentum. So this must be considered with spin - orbit coupling in the form of the HamiltonianIn this paper, the spin-orbital model is studied based on the Heisenberg model, that is, the energy gap of the two-dimensional grid point of the solid in strong interaction. The Hamiltonian of this model has the su (2) ? su(2) symmetry. The main work are the following three areas:First, the spin and isospin are formulated in the form of the four states of the system in the Dirac representation, and then the Hamiltonian expression for raising and lowering operators are derived, it is too complex in the form of the Hamiltonian to solve out its intrinsic value, so it marks in the Single coupling form by the mean field theory.Secondly, the above Hamiltonian is transformed into the inverted form of space by grid Fourier transform and the matrix expression indicated the result is a 8×8 matrix, and by unitary transformation the express is diagonalized, the unitary transformation only changes the description, rather than the system state, it is the transformation between different representations, and the description of the different representation of the system is completely equivalent, so the intrinsic value of Hamiltonian will not change. diagonalization is not only expressed in its own representation, but also the easiest way to describe the system, so a Hamiltonian eigenvalue is got.Again, the partition function of the system is formulated in the form of energy eigenvalues, by which free energy of the system is derivatecan, due to the parameters of Hamiltonian of the system, it is clear that the intrinsic value of the partition and the free energy are functions with the same parameters. to get the extreme value of the parameters in The free energy of the system, there have saddle point equations, the results indicate that they are four sum equations, four integral equations are got by transformation, for the four equations with six parameters, parameters are solved if two parameters are assigned.