Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures

TL;DR

This paper develops a theoretical framework for quantum critical points in graphene heterostructures involving competing Chern insulators, revealing emergent symmetries and making predictions verified by numerical simulations.

Contribution

It introduces a family of QED$_3$-Chern-Simons theories describing critical points between Chern insulators, with emergent SU$(N_f)$ symmetry and experimentally testable predictions.

Findings

Emergent SU$(N_f)$ symmetry at critical points.

Verification of charge density wave predictions via DMRG.

Proposal of experiments to test duality conjectures in 2+1D CFTs.

Abstract

Recent experiments in graphene heterostructures have observed Chern insulators - integer and fractional Quantum Hall states made possible by a periodic substrate potential. Here we study theoretically the competition between different Chern insulators, which can be tuned by the amplitude of the periodic potential, leads to a new family of quantum critical points described by QED$_3$-Chern-Simons theory. At these critical points, $N_f$ flavors of Dirac fermions interact through an emergent U$(1)$ gauge theory at Chern-Simons level $K$, and remarkably, the entire family (with any $N_f$ or $K$) can be realized at special values of the external magnetic field. Transitions between particle-hole conjugate Jain states realize "pure" QED$_3$ in which multiple flavors of Dirac fermion interact with a Maxwell U$(1)$ gauge field. The multi-flavor nature of the critical point leads to an emergent SU$(N_f)$ symmetry. Specifically, at the transition from a $\nu=$1/3 to 2/3 quantum Hall state, the emergent SU(3) symmetry predicts an octet of charge density waves with enhanced susceptibilities, which is verified by DMRG numerical simulations on microscopic models applicable to graphene heterostructures. We propose experiments on Chern insulators that could resolve open questions in the study of 2+1 dimensional conformal field theories and test recent duality inspired conjectures.