The spectral theorem of many-body Green's function theory when there are zero eigenvalues of the matrix governing the equations of motion

摘要

In using the spectral theorem of many-body Green's function theory in orderto relate correlations to commutator Green's functions, it is necessary in thestandard procedure to consider the anti-commutator Green's functions as wellwhenever the matrix governing the equations of motion for the commutatorGreen's functions has zero eigenvalues. We show that a singular-valuedecomposition of this matrix allows one to reformulate the problem in terms ofa smaller set of Green's functions with an associated matrix having no zeroeigenvalues, thus eliminating the need for the anti-commutator Green'sfunctions. The procedure is quite general and easy to apply. It is illustratedfor the field-induced reorientation of the magnetization of a ferromagneticHeisenberg monolayer and it is expected to work for more complicated cases aswell.