Entanglement scaling of fractional quantum Hall states through geometric deformations

Abstract

We present a new approach for obtaining the scaling behavior of the entanglement entropy in fractional quantum Hall (FQH) states from finitesize wavefunctions. By employing the torus geometry and the fact that the torus aspect ratio can be readily varied, we can extract the entanglement entropy of a spatial block as a continuous function of the block boundary length. This approach allows us to extract the topological entanglement entropy with an accuracy superior to that possible for the spherical or disc geometry, where no natural continuously variable parameter is available. Other than the topological information, the study of entanglement scaling is also useful as an indicator of the difficulty posed by FQH states for various numerical techniques. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.