2005/09/06 by F. Mancini, A. Avella · 1 citation
Physics and Astronomy · #cond-mat.str-el #cond-mat.supr-con
paper · pdf · doi:10.1080/00018730412331303722
published as Advances in Physics 53, 537 (2004) · 232 pages, more than 300 figures, more than 500 references
arxiv created 2005/09/06 · arxiv updated 2009/12/01
The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.