Interacting and fractional topological insulators via the ${\mathbb{Z}}_2$ chiral anomaly

Abstract

Recently it was shown that the topological properties of $2D$ and $3D$ topological insulators are captured by a ${\mathbb{Z}}_2$ chiral anomaly in the boundary field theory. It remained, however, unclear whether the anomaly survives electron-electron interactions. We show that this is indeed the case, thereby providing an alternative formalism for treating topological insulators in the interacting regime. We apply this formalism to fractional topological insulators (FTI) via projective/parton constructions and use it to test the robustness of all fractional topological insulators which can be described in this way. The stability criterion we develop is easy to check and based on the pairswitching behaviour of the noninteracting partons. In particular, we find that FTIs based on bosonic Laughlin states and the $M=0$ bosonic Read-Rezayi states are fragile and may have a completely gapped and non-degenerate edge spectrum in each topological sector. In contrast, the ${\mathbb{Z}}_k$ Read-Rezayi states with $M=1$ and odd $k$ and the bosonic $3D$ topological insulator with a $\pi /4$ fractional theta-term are topologically stable.

Added references and fixed typos in ver.2

References in corpus (3)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Fractional topological insulators in three dimensions

Cited by in corpus (9)

• Classification of topological quantum matter with symmetries
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Bosonic Anomalies, Induced Fractional Quantum Numbers and Degenerate Zero Modes: the anomalous edge physics of Symmetry-Protected Topological States
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Fractional Topological Insulators -- a Pedagogical Review
• Conflicting Symmetries in Topologically Ordered Surface States of Three-dimensional Bosonic Symmetry Protected Topological Phases
• ${\mathbb{Z}}_2$ fractional topological insulators in two dimensions
• Global phase diagram of two-component Bose gases in antiparallel magnetic fields
• Stability of Topological Insulators with Non-Abelian Edge Excitations