Equation of Motion Method for Composite Field Operators

Abstract

The Green's function formalism in Condensed Matter Physics is reviewed within the equation of motion approach. Composite operators and their Green's functions naturally appear as building blocks of generalized perturbative approaches and require fully self-consistent treatments in order to be properly handled. It is shown how to unambiguously set the representation of the Hilbert space by fixing both the unknown parameters, which appear in the linearized equations of motion and in the spectral weights of non-canonical operators, and the zero-frequency components of Green's functions in a way that algebra and symmetries are preserved. To illustrate this procedure some examples are given: the complete solution of the two-site Hubbard model, the evaluation of spin and charge correlators for a narrow-band Bloch system, the complete solution of the three-site Heisenberg model, and a study of the spin dynamics in the Double-Exchange model.

20 RevTeX4 pages, 4 embedded figures

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• New perspectives on the Ising model
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• Phase diagrams of half-filled 1D and 2D extended Hubbard model within COM
• The composite operator method route to the 2D Hubbard model and the cuprates
• Effects of two-site composite excitations in the Hubbard model
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