Fractional Chern insulators with a non-Landau level continuum limit

TL;DR

This paper constructs lattice models with bands that remain distinct from Landau levels even in the continuum limit, enabling the study of fractional quantum Hall phases beyond traditional Landau level physics.

Contribution

It introduces new lattice models with unique band geometry that persist in the continuum limit, providing a platform to analyze FQH phases outside Landau level regimes.

Findings

Identified band geometry features influencing FQH stability

Computed a localization length exponent of 2.57(3)

Observed signatures of Laughlin states in the models

Abstract

Recent developments in fractional quantum Hall (FQH) physics highlight the importance of studying FQH phases of particles partially occupying energy bands that are not Landau levels. FQH phases in the regime of strong lattice effects, called fractional Chern insulators, provide one setting for such studies. As the strength of lattice effects vanishes, the bands of generic lattice models asymptotically approach Landau levels. In this article, we construct lattice models for single-particle bands that are distinct from Landau levels even in this continuum limit. We describe how the distinction between such bands and Landau levels is quantified by band geometry over the magnetic Brillouin zone and reflected in the electromagnetic response. We analyze the localization-delocalization transition in one such model and compute a localization length exponent of 2.57(3). Moreover, we study interactions projected to these bands and find signatures of bosonic and fermionic Laughlin states. Most pertinently, our models allow us to isolate conditions for optimal band geometry and gain further insight into the stability of FQH phases on lattices.