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

P. Fröbrich; P. J. Kuntz

doi:10.1103/physrevb.68.014410

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

P. Fröbrich·P. J. Kuntz

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Abstract

In using the spectral theorem of many-body Green's function theory in order to relate correlations to commutator Green's functions, it is necessary in the standard procedure to consider the anti-commutator Green's functions as well whenever the matrix governing the equations of motion for the commutator Green's functions has zero eigenvalues. We show that a singular-value decomposition of this matrix allows one to reformulate the problem in terms of a smaller set of Green's functions with an associated matrix having no zero eigenvalues, thus eliminating the need for the anti-commutator Green's functions. The procedure is quite general and easy to apply. It is illustrated for the field-induced reorientation of the magnetization of a ferromagnetic Heisenberg monolayer and it is expected to work for more complicated cases as well.

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P. Fröbrich, P. J. Kuntz. 2003-05-19. The spectral theorem of many-body Green's function theory when there are zero eigenvalues of the matrix governing the equations of motion. https://doi.org/10.1103/physrevb.68.014410

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