Stability of fractional Chern insulators with a non-Landau level continuum limit

TL;DR

This paper investigates the stability of fractional Chern insulators without a Landau level continuum limit, challenging the geometric stability hypothesis by analyzing many-body spectra and metrics.

Contribution

It demonstrates that the geometric stability hypothesis applies even to Chern bands not connected to Landau levels, expanding understanding of fractional Chern insulator stability.

Findings

The geometric stability hypothesis holds for non-Landau level Chern bands.

Larger system sizes are often needed for convergence in non-Landau level cases.

The relationship between single-particle metrics and many-body gaps is confirmed.

Abstract

The stability of fractional Chern insulators is widely believed to be predicted by the resemblance of their single-particle spectra to Landau levels. We investigate the scope of this geometric stability hypothesis by analyzing the stability of a set of fractional Chern insulators that explicitly do not have a Landau level continuum limit. By computing the many-body spectra of Laughlin states in a generalized Hofstadter model, we analyze the relationship between single-particle metrics, such as trace inequality saturation, and many-body metrics, such as the magnitude of the many-body and entanglement gaps. We show numerically that the geometric stability hypothesis holds for Chern bands that are not continuously connected to Landau levels, as well as conventional Chern bands, albeit often requiring larger system sizes to converge for these configurations.