Entanglement entropy of random fractional quantum Hall systems

Abstract

The entanglement entropy of the ν = 1/3 and ν = 5/2 quantum Hall states in the presence of short-range random disorder has been calculated using direct diagonalization. A microscopic model of electron-electron interaction is used and spin-polarized electrons are confined to a single Landau level and interact with long-range Coulomb interaction. In the case of very weak disorder, the values of topological entanglement entropy are roughly consistent with the expected theoretical results. By considering a broad range of disorder strengths, entanglement entropy was studied in an effort to detect quantum phase transitions. In particular, there is a signature of the transition as the function of the disorder strength for the ν = 5/2 state. Prospects of using the density matrix renormalization group to compute the entanglement entropy for larger system sizes are discussed. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.