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29 March 2024
 
  » arxiv » cond-mat/0305444

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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 ;
Date 19 May 2003
Journal Phys. Rev. B 68, 014410(2003)
Subject Statistical Mechanics; Strongly Correlated Electrons | cond-mat.stat-mech cond-mat.str-el
AbstractIn 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.
Source arXiv, cond-mat/0305444
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