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

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