title: 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 nontrivial quantum geometry.
authors.affiliation: Department of Applied Physics, Stanford University, California 94305, USA.|Stanford Institute for Materials and Energy Sciences, SLAC & Stanford University, Stanford, California 94025, USA.
authors.forename: Martin
authors.initials: M
authors.lastname: Claassen
authors.affiliation: Department of Physics, Stanford University, Stanford, California 94305, USA.
authors.forename: Ching Hua
authors.initials: CH
authors.lastname: Lee
authors.affiliation: Institute for Theoretical Physics and Astrophysics, University of Würzburg, D 97074 Würzburg, Germany.
authors.forename: Ronny
authors.initials: R
authors.lastname: Thomale
authors.affiliation: Department of Physics, Stanford University, Stanford, California 94305, USA.
authors.forename: Xiao-Liang
authors.initials: XL
authors.lastname: Qi
authors.affiliation: Stanford Institute for Materials and Energy Sciences, SLAC & Stanford University, Stanford, California 94025, USA.
authors.forename: Thomas P
authors.initials: TP
authors.lastname: Devereaux