Fractional Chern Insulators beyond Laughlin states

TL;DR

This paper presents the first numerical evidence of composite fermion states in fractional Chern insulators, demonstrating their topological properties and correspondence with fractional quantum Hall states through various analytical approaches.

Contribution

It provides the first numerical observation of CF states in FCI models and explores their topological features, extending the understanding beyond Laughlin states.

Findings

CF states observed at specific filling factors in FCI models

FCI quasihole and quasielectron excitations resemble FQH counterparts

Entanglement spectra match FQH signatures

Abstract

We report the first numerical observation of composite fermion (CF) states in fractional Chern insulators (FCI) using exact diagonalization. The ruby lattice Chern insulator model for both fermions and bosons exhibits a clear signature of CF states at filling factors 2/5 and 3/7 (2/3 and 3/4 for bosons). The topological properties of these states are studied through several approaches. Quasihole and quasielectron excitations in FCI display similar features as their fractional quantum hall (FQH) counterparts. The entanglement spectrum of FCI groundstates shows an identical fingerprint to its FQH partner. We show that the correspondence between FCI and FQH obeys the emergent symmetry already established, proving the validity of this approach beyond the clustered states. We investigate other Chern insulator models and find similar signatures of CF states. However, some of these systems exhibit strong finite size effects.