Time-reversal symmetric hierarchy of fractional incompressible liquids

TL;DR

This paper develops a theoretical framework for fractional topological insulators, extending the fractional quantum Hall effect to time-reversal symmetric systems, and establishes bulk-edge correspondence with explicit edge theories and wave functions.

Contribution

It introduces a hierarchical, time-reversal symmetric effective theory for fractional topological insulators, including the fractional quantum spin Hall effect, with explicit edge theories and wave functions.

Findings

Derived the edge theory for time-reversal symmetric fractional liquids.

Established bulk-edge correspondence for the hierarchical theory.

Provided explicit ground state wave functions for the bulk theory.

Abstract

We provide an effective description of fractional topological insulators that include the fractional quantum spin Hall effect by considering the time-reversal symmetric pendant to the topological quantum field theories that encode the Abelian fractional quantum Hall liquids. We explain the hierarchical construction of such a theory and establish for it a bulk-edge correspondence by deriving the equivalent edge theory for chiral bosonic fields. Further, we compute the Fermi-Bose correlation functions of the edge theory and provide representative ground state wave functions for systems described by the bulk theory.