Hubbard Model as a Simplest Model of Strong Electron Correlations

Sergei G. Ovchinnikov, Valerii Vladimirovich Val'kov

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

Yu. A. Izyumov

Arisato Kawabata

Thomas Maurice Rice

This chapter provides an introduction to the theory of strongly correlated electrons and discusses some of the ideas that presently are being pursued to try to resolve this dilemma. The Hubbard Model is by now surely the most infamous or notorious model problem in solid state physics because the ratio of number of papers to understanding of this model must be an all time record. Yet it is a model which describes the competition between the kinetic energy and the Coulomb interaction in the simplest way. Its origin lies in work of Van Vleck. One tried and true method when have to deal with strong interactions is to look for the right mean-field or Hartree-Fock method. This method has of course been widely applied to the Hubbard Model. The one-dimesional Hubbard model with t not equal to zero for nearest neighbours was solved by Lieb and Wu using Bethe-Ansatz methods.

ARMEN N. KOCHARIAN, P. S. Ovnanyan

M. M. Sánchez, A. Avella, F. Mancini

PACS. 71.10.−w – Theories and models of many electron systems. PACS. 71.10.Fd – Lattice fermion models. PACS. 71.15.Th – Other methods. Abstract. – The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions, which cannot be obtained by means of the Bethe Ansatz, except for some limiting cases. Introduction. – New materials whose physics is dominated by electron correlations in narrow energy bands are actually a challenge for solid state physicists. The treatment of such systems is not trivial due to the competition between itinerant and localized behaviour of the electrons in these bands. The Hubbard Hamiltonian [1] is regarded as the simplest model