Haldane statistics in the finite-size entanglement spectra of 1/m fractional quantum Hall states

Abstract

We conjecture that the counting of the levels in the orbital entanglement spectra (OES) of finite-size Laughlin fractional quantum Hall (FQH) droplets at filling nu = 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 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. We support our conjecture with ample numerical checks.