Bosonization and the Berry connection in two-dimensional QED
  The dynamical effects of topological charge in two-dimensional QED can be expressed in terms of a topological order parameter via a Berry phase construction. The Berry phase describes the electric charge polarization of the vacuum in a manner similar to the theory of polarization in topological insulators. The topological order parameter labels discrete vacua which differ by units of electric flux. Here the associated Berry connection is explicitly constructed from the Dirac Hamiltonian eigenstates by introducing a small attractive Thirring coupling, so that there is still a stable boson in the limit of zero EM coupling. The Berry connection arises from the analytic structure of the Bethe ansatz states in complex rapidity near the free fermion point. 
H. B. Thacker and Gabriel Wong
hep-th hep-lat quant-ph