Mott Transitions: A Brief Review

Abstract

This short review provides an overview of some aspects of the current understanding of Mott insulators and Mott metal-insulator transitions. The development of this field is traced, from earliest classical views to the state-of-the-art picture based on methods of quantum field theory. A quasi-local view point, characterizing “pure” Mott physics, throughout this article is focused on. Following an extensive discussion on Mott transitions in one- and multi-orbital Hubbard models, progress is reviewed in first-principles correlation-based approaches in achieving a quantitative description of insulator-metal transitions in two celebrated Mott materials. Building thereupon, success of such approaches in providing microscopic justification for the famed Mott criterion, as well as in the attempts to model emerging devices is reviewed briefly. The study is concluded with a discussion of a class of Mott insulators modeled by the Kugel-Khomskii model, and discuss how progress in the understanding of novel quantum liquid-crystal-like order provides an attractive opportunity to gain insight into topologically ordered states and topological-to-trivial phase transitions for certain quantum spin models in terms of a dual description in terms of Landau-like symmetry breaking.