Emergent QCD3 quantum phase transitions of fractional Chern insulators

Motivated by the recent work on QED3-Chern-Simons quantum critical points of fractional Chern insulators [Phys. Rev. X 8, 031015 (2018)2160-330810.1103/PhysRevX.8.031015], we study its non-Abelian generalizations, namely, QCD3-Chern-Simons quantum phase transitions of fractional Chern insulators. These phase transitions are described by Dirac fermions interacting with non-Abelian Chern-Simons gauge fields [U(N), SU(N), USp(N), etc.]. Utilizing the level-rank duality of Chern-Simons gauge theory and non-Abelian parton constructions, we discuss two types of QCD3 quantum phase transitions. The first type happens between two Abelian states in different Jain sequences, as opposed to the QED3 transitions between Abelian states in the same Jain sequence. A good example is the transition between σxy=1/3 state and σxy=-1 state, which has Nf=2 Dirac fermions interacting with a U(2) Chern-Simons gauge field. The second type is naturally involving non-Abelian states. For the sake of experimental feasibility, we focus on transitions of Pfaffian-like states, including the Moore-Read Pfaffian, anti-Pfaffian, particle-hole Pfaffian, etc. These quantum phase transitions could be realized in experimental systems such as fractional Chern insulators in graphene heterostructures.