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arXiv:cond-mat/0202313

Superstring representation of Hubbard model

V. M. Zharkov

Published Feb 19, 2002• 1 citation
arXivHTMLPDF

Abstract

The new method of investigation of strongly correlated electronic system is presented. Using this method we have derived thee superstring from 2D Hubbard model. The novel expression for generalized supercoherent state has been calculated.
DOI
10.48550/arxiv.cond-mat/0202313

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The Hubbard model is used to study an electronic system. In this paper we present the new path integral representation for Hubbard model. We have constructed the new supercoherent state which appears from a set of eigenfunctions of atomic limit of strongly correlated systems. Exact calculation of nonlinear representation of a supergroup has been carried. This group defines the transformation of atomic base. The general formalism we elaborate for Hubbard model is the one widely used in the gauge field theory of the nonlinear representation of a superconformal group.
The Hubbard model is used to study an electronic system. In this paper we present the new path integral representation for Hubbard model. We have constructed the new supercoherent state for spinless electrons which appears from a set of eigenfunctions of atomic limit of strongly correlated systems. Exact calculation of nonlinear representation of a supergroup has been carried. This group defines the transformation of atomic base. The general formalism we elaborate for Hubbard model is the one widely used in the gauge field theory of the nonlinear representation of a superconformal group.
Hubbard Model as the Simplest Model of Strong Electron Correlation Multielectron Models in X-Operators Representation General Approach to the Quasiparticle Description of Strongly Correlated Systems Unitary Transformations Method in Atomic Representation Diagram Technique in the X-Operators Representation Spectral Properties of the Anisotropic Metallic Ferromagnets Peculiarities of the de Haas-van Alphen Effect in Strongly Correlated Systems with Magnetic Polaron States The Electronic Structure of Copper Oxides in the Multiorbital p-d Model
A state-of-the-art review is given of the investigations of the Hubbard model, which is the main model used in the theory of strongly correlated electron systems. It is shown how the main correlation effects — the metal–insulator phase transition, the appearance of localised magnetic moments, and the breakdown of the Fermi-liquid behaviour — appear in the case of strong electron correlations when U ~ W, where U is the Coulomb repulsion parameter and W is the band width. Different approaches to the problem, not based on perturbation theory in terms of the parameter U/W or W/U, are presented. A new method in the theory of strongly correlated systems, in which the limit of infinite number of dimensions of space, d = ∞, is the main feature of the review. The physical results obtained by this approach are compared with those deduced by traditional methods. An overview of the behaviour of strongly correlated systems is given for wide ranges of the model parameters U and W, and of the electron density n.
Strongly correlated electron systems with planar structure, like high{Tc superconductors, are currently under intensive study.In the search for a realistic model to describe the anomalous behaviors of these systems, we have studied the 2D Extended Hubbard model by means of the Composite Operator Method.The local properties, the density of states and the Fermi surface have been calculated as functions of the model parameters.Particular attention has been paid to the role played by the intersite interaction V which drives important changes in the electronic properties of the system.