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

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

2003-05-19

arxiv.org/abs/cond-mat/0305444v1

Phys. Rev. B 68, 014410(2003)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 1 figure, accepted for publication in Physical Review B (16. May 2003)

Scientific paper

10.1103/PhysRevB.68.014410

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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