Abstract
Motivated by the recent work of QED₃-Chern-Simons quantum critical points of fractional Chern insulators (Phys. Rev. X \textbf{8}, 031015, (2018)), 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 σ^xy=1/3 state and σ^xy=-1 state, which has N_f=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.