Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory

TL;DR

This paper uses the sliding Luttinger liquids approach to analyze fractional topological insulators, revealing their low-energy fixed point, the impact of interactions on topological phases, and the emergence of Chern-Simons terms from chiral anomalies.

Contribution

It demonstrates that fractional topological insulators can be described as a low-energy fixed point using sliding Luttinger liquids and connects chiral anomalies to Chern-Simons theory.

Findings

FTI is the low-energy fixed point of the theory.

Interactions can extend the topological phase boundaries.

Chiral anomaly leads to Chern-Simons terms in the effective gauge theory.

Abstract

The sliding Luttinger liquids (LL) approach is applied to study fractional topological insulators (FTI). We show that FTI is the low energy fixed point of the theory for realistic spin-orbit and electron-electron interaction. We find that the topological phase pertains in the presence of interaction that breaks the spin invariance and its boundaries are even extended by those terms. Finally we show that one dimensional chiral anomaly in the LL leads to the emergence of topological Chern-Simons terms in the effective gauge theory of the FTI state.