A Concrete Example of Fractional Chern Insulator

TL;DR

This paper provides a concrete example of a fractional Chern insulator on a square lattice, demonstrating fractional quantization of Hall conductance and exploring related charge density wave order.

Contribution

It introduces specific lattice models with finite-range hopping and interactions that realize fractional Chern insulators with quantized Hall conductance.

Findings

Hall conductance is fractionally quantized to 1/2 at 3/8 filling.

Presence of long-range charge density wave order with Chern number 1.

Finite-range interactions can produce fractional Chern insulator states.

Abstract

We present a concrete example of fractional Chern insulator whose fermion Hamiltonian consists of hopping and Coulomb repulsive interaction terms. Both of them are of finite range on the square lattice. In a strong coupling limit for the interaction Hamiltonian, we show that the Hall conductance is fractionally quantized to $1/2$ in the sense of the expectation value with respect to the four-fold degenerate ground state at the filling $3/8$. We also present a slightly different example in which there appears a long-range order of charge density wave with the Chern number $1$.