Understanding correlated electron systems by a classification of Mott insulators

This article surveys the physics of systems proximate to Mott insulators, and presents a classification using conventional and topological order parameters. This classifi-cation offers a valuable perspective on a variety of conducting correlated electron systems, from the cuprate superconductors to the heavy fermion compounds. Con-nections 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 fraction-alization of bosonic collective modes. Two distinct categories of Z2 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).