Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators

TL;DR

This paper reports the discovery of new Abelian and non-Abelian topological states in fractional Chern insulators with Chern number C≥1, characterized by specific filling fractions and matching FQH state counting, supported by energy and entanglement spectra.

Contribution

The study identifies a new series of topological states in FCIs at fractional fillings, providing evidence for their Abelian or non-Abelian nature and analyzing their spectral properties.

Findings

Identification of Abelian and non-Abelian states at specific fillings.

Spectral evidence matching FQH state counting and degeneracies.

Entanglement spectrum analysis supporting SU(C) color-singlet states.

Abstract

We report the observation of a new series of Abelian and non-Abelian topological states in fractional Chern insulators (FCI). The states appear at bosonic filling nu= k/(C+1) (k, C integers) in several lattice models, in fractionally filled bands of Chern numbers C>=1 subject to on-site Hubbard interactions. We show strong evidence that the k=1 series is Abelian while the k>1 series is non-Abelian. The energy spectrum at both groundstate filling and upon the addition of quasiholes shows a low-lying manifold of states whose total degeneracy and counting matches, at the appropriate size, that of the Fractional Quantum Hall (FQH) SU(C) (color) singlet k-clustered states (including Halperin, non-Abelian spin singlet states and their generalizations). The groundstate momenta are correctly predicted by the FQH to FCI lattice folding. However, the counting of FCI states also matches that of a spinless FQH series, preventing a clear identification just from the energy spectrum. The entanglement spectrum lends support to the identification of our states as SU(C) color-singlets but offers new anomalies in the counting for C>1, possibly related to dislocations that call for the development of new counting rules of these topological states.