A comprehensive introduction about strongly correlated electronic phenomena

Abstract

The electron gas model proposed by Fermi in 1926 constitutes one of the first direct applications of Quantum Mechanics in the description of the physical properties of solids. In particular, the mathematical description of the electronic contribution to the specific heat is a hallmark in this field. However, exotic manifestations of matter cannot be described by the Fermi gas model and band theory. Examples include the Mott insulating phase and the enhancement of the Sommerfeld coefficient for the so-called heavy fermions systems. In this contribution, we revisit comprehensively fundamental concepts related to strongly correlated electronic phenomena. We focus on an analysis of the Hubbard model for the Mott dimer in a direct connection with current research topics and experimental observations. We also revisit the Fermi-Hubbard, Bose-Fermi-Hubbard, Anderson
single-impurity, Su–Schrieffer–Heeger, t-J, and RVB models, as well as the BCS theory and density functional theory and its applications. Yet, the dynamical mean-field theory and the GW approximation are briefly discussed. The present work can be seen as a primer for a broad audience interested in the theoretical and experimental aspects related to research in the field of strongly correlated electronic systems.