title: Correlation lengths and topological entanglement entropies of unitary and nonunitary fractional quantum Hall wave functions.
abstract: Using the newly developed matrix product state formalism for non-Abelian fractional quantum Hall (FQH) states, we address the question of whether a FQH trial wave function written as a correlation function in a nonunitary conformal field theory (CFT) can describe the bulk of a gapped FQH phase. We show that the nonunitary Gaffnian state exhibits clear signatures of a pathological behavior. As a benchmark we compute the correlation length of a Moore-Read state and find it to be finite in the thermodynamic limit. By contrast, the Gaffnian state has an infinite correlation length in (at least) the non-Abelian sector, and is therefore gapless. We also compute the topological entanglement entropy of several non-Abelian states with and without quasiholes. For the first time in the FQH effect the results are in excellent agreement in all topological sectors with the CFT prediction for unitary states. For the nonunitary Gaffnian state in finite size systems, the topological entanglement entropy seems to behave like that of the composite fermion Jain state at equal filling.
authors.affiliation: Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005 Paris, France.|CNRS, UMR 7589, LPTHE, F-75005 Paris, France.
authors.forename: B
authors.initials: B
authors.lastname: Estienne
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.|Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France.
authors.forename: N
authors.initials: N
authors.lastname: Regnault
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: B A
authors.initials: BA
authors.lastname: Bernevig