Conformal QED in two-dimensional topological insulators

TL;DR

This paper derives a gauge-theory-based model for the helical Luttinger liquid phase in two-dimensional topological insulators, connecting edge state interactions with conformal quantum electrodynamics and the Thirring model.

Contribution

It provides a first-principles derivation of the helical Luttinger liquid phase using gauge theory and conformal QED, linking microscopic interactions to effective field theories.

Findings

Derivation of a gauge theory for edge states mediated by a dynamical electromagnetic field.

Mapping of the gauge theory to a 1+1D Thirring model via bosonization.

Identification of the HLL parameters as functions of the fine-structure constant.

Abstract

It has been shown recently that local four-fermion interactions on the edges of two-dimensional time-reversal-invariant topological insulators give rise to a new non-Fermi-liquid phase, called helical Luttinger liquid (HLL). In this work, we provide a first-principle derivation of this non-Fermi-liquid phase based on the gauge-theory approach. Firstly, we derive a gauge theory for the edge states by simply assuming that the interactions between the Dirac fermions at the edge are mediated by a quantum dynamical electromagnetic field. Here, the massless Dirac fermions are confined to live on the one-dimensional boundary, while the (virtual) photons of the U(1) gauge field are free to propagate in all the three spatial dimensions that represent the physical space where the topological insulator is embedded. We then determine the effective 1+1-dimensional conformal field theory (CFT) given by the conformal quantum electrodynamics (CQED). By integrating out the gauge field in the corresponding partition function, we show that the CQED gives rise to a 1+1-dimensional Thirring model. The bosonized Thirring Hamiltonian describes exactly a HLL with a parameter K and a renormalized Fermi velocity that depend on the value of the fine-structure constant $\alpha$.