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In the equation of motion approach to the two-time Green's functions,conventional Tyablikov-type truncation of the chain of equations is ratherarbitrary and apt to violate the analytical structure of Green's functions.Here, we propose a practical way to truncate the equations of motion usingoperator projection. The partial projection approximation is introduced toevaluate the Liouville matrix. It guarantees the causality of Green'sfunctions, fulfills the time translation invariance and the particle-holesymmetry, and is easy to implement in a computer. To benchmark this method, westudy the Anderson impurity model using the operator basis at the level ofLacroix approximation. Improvement over conventional Lacroix approximation isobserved. The distribution of Kondo screening in the energy space is studiedusing this method.

Projective Truncation Approximation for Equations of Motion of Two-Time Green's Functions