Characterization and stability of a fermionic ν=1/3 fractional Chern insulator

Using the infinite density matrix renormalization group method on an infinite cylinder geometry, we characterize the 1/3 fractional Chern insulator state in the Haldane honeycomb lattice model at nu = 1/3 filling of the lowest band and check its stability. We investigate the chiral and topological properties of this state through (i) its Hall conductivity, (ii) the topological entanglement entropy, (iii) the U(1) charge spectral flow of the many-body entanglement spectrum, and (iv) the charge of the anyons. In contrast to numerical methods restricted to small finite sizes, the infinite cylinder geometry allows us to access and characterize directly the metal to fractional Chern insulator transition. We find indications it is first order and no evidence of other competing phases. Since our approach does not rely on any band or subspace projection, we are able to prove the stability of the fractional state in the presence of interactions exceeding the band gap, as has been suggested in the literature. As a by-product we discuss the signatures of Chern insulators within this technique.