Zoology of Fractional Chern Insulators

TL;DR

This paper investigates fractional Chern insulators across various models, demonstrating the emergence of Laughlin-like and Moore-Read states through numerical analysis of energy and entanglement spectra, highlighting key band structure features.

Contribution

It provides a comparative study of different Chern insulator models showing how topological phases emerge under strong interactions and tuning of band parameters.

Findings

All models exhibit Laughlin-like phase at 1/3 filling

Some models host a phase similar to the nu=1/2 Pfaffian Moore-Read state

Entanglement spectra reveal cluster correlations

Abstract

We study four different models of Chern insulators in the presence of strong electronic repulsion at partial fillings. We observe that all cases exhibit a Laughlin-like phase at filling fraction 1/3. We provide evidence of such a strongly correlated topological phase by studying both the energy and the entanglement spectra. In order to identify the key ingredients of the emergence of Laughlin physics in these systems, we show how they are affected when tuning the band structure. We also address the question of the relevance of the Berry curvature flatness in this problem. Using three-body interactions, we show that some models can also host a topological phase reminiscent of the nu=1/2 Pfaffian Moore-Read state. Additionally, we identify the structures indicating cluster correlations in the entanglement spectra.