Visualizing the Mott transition

Abstract

Correlated electronic systems involve strong short-range repulsion. At integer filling, the primary effect of correlation is the emergence of an insulating state where band theory predicts a metal. Understanding the transition from a metal to this ‘Mott insulator’, as interaction strength is increased, and the effect of doping the Mott state, are classic problems in quantum many-body physics. They have been explored for decades, starting with the approximate solutions of Hubbard. The real breakthrough came in the 1990s with the advent of dynamical mean field theory, which mapped the correlated system to an embedded single site, and described the detailed spectral evolution across the Mott transition. The only deficiency in this approach is the neglect of spatial correlations, and, possibly, the lack of some ‘visual intuition’ about the transition. We discuss a complementary approach, which provides a reasonable description of Mott physics in a real-space setting and allows a certain degree of visualization. This article provides a pedagogical review of our approach and presents some illustrative results.