Effective hydrodynamic field theory and condensation picture of topological insulators

TL;DR

This paper develops a hydrodynamic effective field theory for 3+1D topological insulators using functional bosonization, describing them as a condensation phase of gauge fields and exploring surface and fractional variants.

Contribution

It introduces a novel hydrodynamic field theory for topological insulators in 3+1D, employing functional bosonization and gauge duality, extending the understanding beyond single-particle descriptions.

Findings

Formulated a two-form gauge field theory for topological insulators.

Described topological insulators as a monopole condensation phase.

Discussed the hydrodynamic surface theory and fractional topological insulators.

Abstract

While many features of topological band insulators are commonly discussed at the level of single-particle electron wave functions, such as the gapless Dirac spectrum at their boundary, it remains elusive to develop a {\it hydrodynamic} or {\it collective} description of fermionic topological band insulators in 3+1 dimensions. As the Chern-Simons theory for the 2+1-dimensional quantum Hall effect, such a hydrodynamic effective field theory provides a universal description of topological band insulators, even in the presence of interactions, and that of putative fractional topological insulators. In this paper, we undertake this task by using the functional bosonization. The effective field theory in the functional bosonization is written in terms of a two-form gauge field, which couples to a $U(1)$ gauge field that arises by gauging the continuous symmetry of the target system (the $U(1)$ particle number conservation). Integrating over the $U(1)$ gauge field by using the electromagnetic duality, the resulting theory describes topological band insulators as a condensation phase of the $U(1)$ gauge theory (or as a monopole condensation phase of the dual gauge field). The hydrodynamic description, and the implication of its duality, of the surface of topological insulators are also discussed. We also touch upon the hydrodynamic theory of fractional topological insulators by using the parton construction.