Understanding correlated electron systems by a classification of Mott insulators

This paper 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 paper (S. Sachdev, cond-mat/0211005). (C) 2002 Elsevier Science (USA). All rights reserved.