Model Fractional Chern Insulators

TL;DR

This paper constructs local lattice models with exact ground states representing fractional Chern insulators, including Abelian and non-Abelian topologically ordered states, useful for studying novel quantum phenomena and guiding experiments.

Contribution

It introduces exact parent Hamiltonians for fractional Chern insulators with higher Chern numbers and parafermion states, advancing the modeling of topologically ordered lattice systems.

Findings

Exact models for fractional Chern insulators with various topological orders.

Ground states are frustration free and reside in the lowest band.

Models are suitable for experimental realization and studying defect phenomena.

Abstract

We devise local lattice models whose ground states are model fractional Chern insulators---Abelian and non-Abelian topologically ordered states characterized by exact ground state degeneracies at any finite size and infinite entanglement gaps. Most saliently, we construct exact parent Hamiltonians for two distinct families of bosonic lattice generalizations of the $\mathcal{Z}_k$ parafermion quantum Hall states: (i) color-entangled fractional Chern insulators at band filling fractions $\nu=k/(\mathcal{C}+1)$ and (ii) nematic states at $\nu=k/2$, where $\mathcal{C}$ is the Chern number of the lowest band in our models. In spite of a fluctuating Berry curvature, our construction is partially frustration free: the ground states reside entirely within the lowest band and exactly minimize a local $(k+1)$-body repulsion term by term. In addition to providing the first known models hosting intriguing states such as higher Chern number generalizations of the Fibonacci anyon quantum Hall states, the remarkable stability and finite-size properties make our models particularly well-suited for the study of novel phenomena involving e.g. twist defects and proximity induced superconductivity, as well as being a guide for designing experiments.