Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators

Abstract

We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as duals of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.

10 pages, 2 figures. Accepted version

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Cited by in corpus (9)

• Topological Photonics
• Topological quantum matter in synthetic dimensions
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Steady-state Hall response and quantum geometry of driven-dissipative lattices
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Fractional Chern Insulators in Singular Geometries
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Exact Mappings in Condensed Matter Physics