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arXiv:cond-mat/0006377 · The European Physical Journal B

Equation of motion method for composite field operators

F. Mancini, Adolfo Avella

Published Nov 1, 2003• 32 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2003-00315-0

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A well-established method to deal with highly correlated systems is based on the expansion of the Green's function in terms of spectral moments. In the context of the Composite Operator Method one approximation is proposed: a set of n composite fields is assumed as fundamental basis and the dynamics is considered up to the order s. The resulting Green's function has a sn-pole structure. The truncation of the hierarchy of the equations of motion is made at the s-th order and the first s-1 equations are treated exactly. A theorem, which rules the conservation of the spectral moments, is presented. The procedure is applied to the Hubbard model and a recurrence relation for the calculation of its electronic spectral moments is derived.
A formalism for the study of highly interacting electronic systems is presented. The proposed scheme is based on two key concepts: composite operators and algebra constraints. Composite field operators, that naturally appear as a consequence of interaction, are promoted to the rank of basic fields in terms of which a perturbation formulation is set up. The formalism is based on the use of Green’s function and equation of motion method. The use of composite operators requires a revisitation of the Green’s function formulation, where the representation is determined by means of algebra constraints which are a manifestation at macroscopic level of the algebra rules and symmetry properties obeyed at microscopic level.
A second-quantized representation for nonrelativistic systems with composite particles is given in which composite particles of two-fermion constituents are described as elementary bosons. The Tani transformation of Girardeau is used to introduce elementary composite fields. An equivalent linear equation of motion method—introducing a ’’d matrix’’—is used in place of the usual nonlinear equation of motion method. This and a diagram formalism are developed to calculate a Hamiltonian and subsidiary condition for this model system and to derive some properties of the Tani transformation.