Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States

TL;DR

This paper proves that fractional Chern insulators can be adiabatically connected to fractional quantum Hall states, establishing their topological equivalence using a formal, thermodynamic-limit-robust approach with hybrid Wannier orbitals.

Contribution

The authors provide a formal proof of the topological equivalence between fractional Chern insulators and fractional quantum Hall states, extending previous evidence to the thermodynamic limit.

Findings

Fractional Chern insulators are adiabatically connected to fractional quantum Hall states.

The proof uses hybrid Wannier orbitals to interpolate between models.

Ground state of bosons in the Haldane model's Chern band connects to Laughlin state.

Abstract

We show how the phases of interacting particles in topological flat bands, known as fractional Chern insulators, can be adiabatically connected to incompressible fractional quantum Hall liquids in the lowest Landau-level of an externally applied magnetic field. Unlike previous evidence suggesting the similarity of these systems, our approach enables a formal proof of the equality of their topological orders, and furthermore this proof robustly extends to the thermodynamic limit. We achieve this result using the hybrid Wannier orbital basis proposed by Qi [Phys. Rev. Lett. 107, 126803 (2011)] in order to construct interpolation Hamiltonians that provide continuous deformations between the two models. We illustrate the validity of our approach for the groundstate of bosons in the half filled Chern band of the Haldane model, showing that it is adiabatically connected to the $\nu=1/2$ Laughlin state of bosons in the continuum fractional quantum Hall problem.