Fifty years of the Hubbard model, from magnetism and

metal-insulator transitions to superconductivity and cold atoms 

Abstract

In 1963 John Hubbard published a novel treatment of a model for fermions in a narrow energy band with strong short-range interactions. It was originally aimed at understanding ferromagnetism in transition metals but its most striking result was a crude description of the metal-insulator (Mott) transition which occurs in systems such as transition metal oxides. In 1964 Hubbard gave a better theory of this transition with an improved solution of his model in which he invented a many-body coherent potential approximation (CPA). The one-electron CPA, later used extensively for calculating the electronic structure of alloys, did not yet exist.

The many-body CPA paved the way for dynamical mean-field theory (DMFT) which came nearly 30 years later and gave the first satisfactory theory of the metal-insulator transition. DMFT is now used routinely for realistic calculations of the electronic structure of strongly-correlated electron systems. These developments, together with some personal reminiscences of John Hubbard from our student days onwards, form the first part of the present talk. There have been two major revivals of interest in the Hubbard model since the early days. The first followed the discovery in 1986 of high temperature superconductivity in doped copper oxides and Anderson’s immediate use of the Hubbard model as a vehicle for his resonating valence bond theory of  these materials. The relevance of the Hubbard model to high temperature superconductivity is still controversial and will be discussed. The second Hubbard model renaissance came in  the 2000s with its experimental realisation by cold atoms in optical lattices. Recent developments will be discussed.

Data: 13 de março

Hora: 11 h (será servido um pequeno lanche às 10:30 h)

Local: Instituto de Física - Sala 343-A

David M. Edwards

Imperial College, London