The Hubbard model within the equations of motion approach

TL;DR

This paper applies the Equations of Motion approach, specifically the Composite Operator Method, to analyze the Hubbard model, providing insights into its properties and relevance to cuprate superconductor behaviors.

Contribution

It systematically employs the Composite Operator Method to study the Hubbard model across various parameters, comparing results with other techniques and simulations.

Findings

Reveals the Hubbard model's capability to describe anomalous cuprate behaviors

Provides comprehensive analysis of local and thermodynamic properties

Validates the analytical approach against known limits and numerical data

Abstract

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.