Fifty years of Hubbard and Anderson lattice models: from magnetism to unconventional superconductivity - A brief overview

TL;DR

This paper reviews fifty years of Hubbard and Anderson lattice models, highlighting their evolution from explaining magnetism to describing unconventional superconductivity, and presents recent results and experimental comparisons.

Contribution

It provides a comprehensive overview of the models' development and introduces new findings on unconventional superconductivity based on real-space pairing mechanisms.

Findings

New results on unconventional superconductivity from recent research

Comparison of theoretical models with experimental data

Insights into real-space pairing mechanisms in correlated systems

Abstract

We briefly overview the importance of Hubbard and Anderson-lattice models as applied to explanation of high-temperature and heavy-fermion superconductivity. Application of the models during the last two decades provided an explanation of the paired states in correlated fermion systems and thus extended essentially their earlier usage to the description of itinerant magnetism, fluctuating valence, and the metal-insulator transition. In second part, we also present some of the new results concerning the unconventional superconductivity and obtained very recently in our group. A comparison with experiment is also discussed, but the main emphasis is put on rationalization of the superconducting properties of those materials within the real-space pairing mechanism based on either kinetic exchange and/or Kondo-type interaction combined with the electron correlation effects.