Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States

ORAL

Abstract

We conjecture that the counting of the levels in the orbital entanglement spectra (OES) of finite-sized Laughlin Fractional Quantum Hall (FQH) droplets at filling 1/m is described by the Haldane statistics of particles in a box of finite size. This principle explains the observed deviations of the OES counting from the edge-mode conformal field theory counting and directly provides us with a topological number of the FQH states inaccessible in the thermodynamic limit- the boson compactification radius. It also suggests that the entanglement gap in the Coulomb spectrum in the conformal limit protects a universal quantity- the statistics of the state.

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Authors

  • Maria Hermanns

    • Princeton University

  • A. Chandran

    • Princeton University, Princeton, NJ 08544
    • Princeton University

  • Nicolas Regnault

    • Laboratoire Pierre Aigrain, Ecole Normale Superieure, CNRS
    • ENS Paris
    • Ecole Normale Superieure, CNRS
    • Laboratoire Pierre Aigrain, ENS and CNRS

  • Andrei Bernevig

    • Department of Physics, Princeton University, Princeton, NJ 08544
    • Princeton University