The Hubbard dimer within the Green's function equation of motion approach

We consider a formulation of the equation of motion technique for Green's function in which the unknown averages are computed by solving a linear system. This linear system appears solvable for all finite temperatures, but depending on the system parameters the condition number can be very large, making the solution numerically unfeasible at low temperatures. In the example that we consider, the Hubbard dimer, we can get rid of this problem by making use of total spin as a good quantum number.