Emergent QCD_{3} quantum phase transitions of fractional Chern insulators

Abstract

Motivated by the recent work on QED_{3}-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, QCD_{3}-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 QCD_{3} quantum phase transitions. The first type happens between two Abelian states in different Jain sequences, as opposed to the QED_{3} 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.