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

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.

15 pages, 9 figures

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• Quantum Geometry and Stabilization of Fractional Chern Insulators Far from the Ideal Limit
• Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture
• Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene
• Single-particle spectral function of fractional quantum anomalous Hall states
• Universal Wilson Loop Bound of Quantum Geometry
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Computing the ${\mathbb{Z}}_2$ Invariant in Two-Dimensional Strongly-Correlated Systems
• Isolated nearly flat higher Chern band in monolayer transition metal trihalides
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
• Effects of the Hubbard interaction on the quantum metric
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Gaplessness from disorder and quantum geometry in gapped superconductors