Bulk-edge correspondence in fractional Chern insulators

TL;DR

This paper develops a new approach to study fractional Chern insulators using a gauge-fixed Wannier-Qi construction in cylinder geometry, enabling analysis of edge states and bulk-edge correspondence with larger systems via DMRG.

Contribution

It introduces a generalized Wannier-Qi method in cylinder geometry, facilitating the study of edge physics and entanglement in fractional Chern insulators with larger system sizes.

Findings

Edge states and entanglement spectra reveal bulk-edge correspondence.

Non-Abelian phase at filling ν=1 can be stabilized by on-site interactions.

Method successfully applied to ruby and kagome lattice models.

Abstract

It has been recently realized that strong interactions in topological Bloch bands give rise to the appearance of novel states of matter. Here we study connections between these systems -- fractional Chern insulators and the fractional quantum Hall states -- via generalization of a gauge-fixed Wannier-Qi construction in the cylinder geometry. Our setup offers a number of important advantages compared to the earlier exact diagonalization studies on a torus. Most notably, it gives access to edge states and to a single-cut orbital entanglement spectrum, hence to the physics of bulk-edge correspondence. It is also readily implemented in the state-of-the-art density matrix renormalisation group method that allows for numerical simulations of significantly larger systems. We demonstrate our general approach on examples of flat-band models on ruby and kagome lattices at bosonic filling fractions $\nu=1/2$ and $\nu=1$, which show the signatures of (non)-Abelian phases, and establish the correspondence between the physics of edge states and the entanglement in the bulk. Notably, we find that the non-Abelian $\nu=1$ phase can be stabilized by purely on-site interactions in the presence of a confining potential.