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Projection Operator Method

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Strongly Correlated Systems

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 171))

Abstract

A general projection operator method in the equation of motion method for the two-time Green functions is formulated. An exact Dyson equation for an arbitrary Green function is derived. The method is used to consider the single-particle electron Green functions for the Hubbard model within the non-crossing approximation for the self-energy. Strong-coupling superconductivity theory for the model is formulated and an equation for the superconducting T c is analyzed. We argue that the d-wave pairing with high-T c can occur in the repulsive Hubbard model, which is mediated by the antiferromagnetic exchange interaction and the spin-fluctuation scattering, both induced by the kinematic interaction for the Hubbard operators. A microscopic theory for the dynamic spin susceptibility within the projection operator method is formulated. The theory is applied to study spin-excitation spectrum for the t–J model within the mode-coupling approximation for the self-energy. A new approach to the theory of the magnetic resonance mode in cuprate superconductors is proposed.

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Authors and Affiliations

  1. Joint Institute for Nuclear Researech, Dubna, Moscow region, 141980, Russia

    Nikolay M. Plakida

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  1. Nikolay M. Plakida
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Correspondence to Nikolay M. Plakida .

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  1. Dipartimento di Fisica "E.R. Caianiello", Università degli Studi di Salerno, Via Ponte don Melillo, Fisciano (SA), 84084, Italy

    Adolfo Avella

  2. Dipartimento di Fisica "E.R. Caianiello", Università degli Studi di Salerno, Via Ponte don Melillo, Fisciano (SA), 84084, Italy

    Ferdinando Mancini

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Plakida, N.M. (2012). Projection Operator Method. In: Avella, A., Mancini, F. (eds) Strongly Correlated Systems. Springer Series in Solid-State Sciences, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21831-6_6

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  • DOI: https://doi.org/10.1007/978-3-642-21831-6_6

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