Topological order, emergent gauge fields, and Fermi surface reconstruction.

This review describes how topological order associated with the presence of emergent gauge elds can reconstruct Fermi surfaces of metals, even in the absence of translational symmetry breaking. We begin with an introduction to topological order using Wegner's quantum Z2 gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying Z2 magnetic 
 ux. The interplay between topological order and the breaking of global symmetry is described by the non-zero temperature statistical mechanics of classical XY models in dimension
 D = 3; such models also describe the zero temperature quantum phases of bosons with
 short-range interactions on the square lattice at integer lling. The topological state
 is again characterized by the expulsion of certain defects, in a state with 
 uctuating
 symmetry-breaking order, along with the presence of emergent gauge elds. The phase
 diagrams of the Z2 gauge theory and the XY models are obtained by embedding them
 in U(1) gauge theories, and by studying their Higgs and conning phases. These
 ideas are then applied to the single-band Hubbard model on the square lattice. A
 SU(2) gauge theory describes the 
 uctuations of spin-density-wave order, and its
 phase diagram is presented by analogy to the XY models. We obtain a class of zero
 temperature metallic states with 
 uctuating spin-density wave order, topological order
 associated with defect expulsion, deconned emergent gauge elds, reconstructed Fermi
 surfaces (with `chargon' or electron-like quasiparticles), but no broken symmetry. Continued in PDF...