Fractional Chern Insulators from the nth Root of Bandstructure

TL;DR

This paper develops a parton-based theoretical framework for fractional Chern insulators, enabling the derivation of wavefunctions and effective theories directly from microscopic lattice models, validated through strong coupling expansions.

Contribution

It introduces a novel parton construction and strong coupling expansion method to connect microscopic lattice models with fractional Chern insulator phases.

Findings

Wavefunctions in the same phase as observed fractional Chern insulators without tuning parameters.

Application of the method to Hofstadter and checkerboard lattice models.

Reliable mapping from microscopic models to effective parton descriptions.

Abstract

We provide a parton construction of wavefunctions and effective field theories for fractional Chern insulators. We also analyze a strong coupling expansion in lattice gauge theory that enables us to reliably map the parton gauge theory onto the microsopic Hamiltonian. We show that this strong coupling expansion is useful because of a special hierarchy of energy scales in fractional quantum Hall physics. Our procedure is illustrated using the Hofstadter model and then applied to bosons at 1/2 filling and fermions at 1/3 filling in a checkerboard lattice model recently studied numerically. Because our construction provides a more or less unique mapping from microscopic model to effective parton description, we obtain wavefunctions in the same phase as the observed fractional Chern insulators without tuning any continuous parameters.