Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence

Abstract

In contemporary physics, especially in condensed matter physics, fermionic topological order and its protected edge modes are one of the most important objects. In this work, we propose a systematic construction of the cylinder partition corresponding to the fermionic fractional quantum Hall effect (FQHE) and a general mechanism for obtaining the candidates of the protected edge modes. In our construction, when the underlying conformal field theory has the $Z_{2}$ duality defects corresponding to the fermionic $Z_{2}$ electric particle, we show that the FQH partition function has a fermionic T duality. This duality is analogous to (hopefully the same as) the dualities in the dual resonance models, typically known as supersymmetry, and gives a renormalization group (RG) theoretic understanding of the topological phases. We also introduce a modern understanding of bulk topological degeneracies and topological entanglement entropy. This understanding is based on the traditional tunnel problem and the recent conjecture of correspondence between the bulk renormalization group flow and the boundary conformal field theory. Our formalism gives an intuitive and general understanding of the modern physics of the topologically ordered systems in the traditional language of RG and fermionization.