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

Abstract

We briefly overview the importance of the Hubbard- and Anderson-lattice models as applied to the 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 essentially extended their earlier usage to the description of itinerant magnetism, fluctuating valence, and the metal-insulator transition. We also present some of the new results concerning the unconventional superconductivity 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.

Keywords:

• real space pairing
• high temperature superconductivity
• heavy fermion superconductivity
• Hubbard model
• Anderson lattice model
• strongly correlated systems

Acknowledgements

I am very grateful to my former and present Ph.D. students: Jakub Jȩdrak, Jan Kaczmarczyk, Olga Howczak, Marcin Abram, Marcin Wysokiński, and Ewa K a̧ dzielawa-Major, for discussions and making available some of the results of our joint or still unpublished works. I thank also to Danuta Goc-Jagło for her technical help.

Additional information

Funding

This work was supported by the Foundation for Polish Science (FNP) through Grant TEAM, as well as by the National Science Centre (NCN) through Grant MAESTRO, No. DEC-2012/04/A/ST3/00342. I thank to Peter Riseborough for his help in editing this and other articles in this special issue.