Bosonization and the Berry connection in two-dimensional QED

TL;DR

This paper explores how topological charge effects in two-dimensional QED can be understood through a Berry phase framework, linking vacuum polarization to topological order parameters and explicitly constructing the Berry connection from Dirac eigenstates.

Contribution

It introduces a novel Berry phase approach to topological charge in 2D QED and explicitly constructs the Berry connection from Bethe ansatz states.

Findings

Berry phase describes vacuum polarization similarly to topological insulators.

Topological order parameter labels discrete vacua with different electric flux.

Berry connection derived from Dirac eigenstates near free fermion point.

Abstract

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.