Understanding correlated electron systems by a classification of Mott insulators

TL;DR

This paper classifies Mott insulators using order parameters, providing insights into correlated electron systems like cuprates and heavy fermions, and discusses topological and conventional orders with experimental implications.

Contribution

It introduces a classification scheme for Mott insulators based on both conventional and topological order parameters, linking various correlated electron phenomena.

Findings

Classification of Mott insulators using order parameters

Connection between magnetic order, fractionalization, and Fermi surface violations

Use of Z_2 gauge theories to describe order interplay

Abstract

This article surveys the physics of systems proximate to Mott insulators, and presents a classification using conventional and topological order parameters. This classification offers a valuable perspective on a variety of conducting correlated electron systems, from the cuprate superconductors to the heavy fermion compounds. Connections are drawn, and distinctions made, between collinear/non-collinear magnetic order, bond order, neutral spin 1/2 excitations in insulators, electron Fermi surfaces which violate Luttinger's theorem, fractionalization of the electron, and the fractionalization of bosonic collective modes. Two distinct categories of Z_2 gauge theories are used to describe the interplay of these orders. Experimental implications for the cuprates are briefly noted, but these appear in more detail in a companion review article (S. Sachdev, cond-mat/0211005).