Extracting the topological entropy for a particle-hole symmetric ansatz of the fractional quantum hall effect in the half-filled second Landau level

POSTER

Abstract

Quantum entanglement measurements have proven useful in characterizing many-body quantum states. In particular, entanglement entropy is a highly effective tool for probing topological order. In this work, we estimate the topological entanglement entropy for a particle-hole symmetric ansatz of the fractional quantum hall effect in the half-filled second Landau level. As a preliminary measure we characterize the parent Hamiltonian, in terms of Haldane pseudopotentials, that produces the particle-hole symmetric ansatz as its exact ground state. We then probe its topological order by estimating the topological entanglement entropy. We find the topological entanglement entropy to be $1.2 \pm 0.4$ (the non-Abelian Moore-Read Pfaffian state has topological entanglement entropy of $\gamma = \ln(8)/2 \approx 1.04$ for comparison).

Authors

  • John McCord

    California State University Long Beach

  • Chi-Yu Hu

    University of California - Berkeley, National Institute for Materials Science, Caifornia State University, Long Beach, University of Michigan, Stockholm University, California State University, Long Beach, Utrecht University, Carl von Ossietzky University of Oldenburg, Germany, Hartnell Community College, Department of Physics, Stockholm University, GRAPPA, University of Amsterdam, Paul Scherrer Institute, Switzerland, California State University, Fresno, California State University Long Beach, Cal State Univ- Long Beach, University of Nevada, Reno, University of Rogensberg, Germany, Tribhuvan University, Nepal, University of Victoria and Perimeter Institute for Theoretical Physics, Institute of Physics, Jagiellonian University, Helmholtz Institute Mainz, Johannes Gutenberg University, Physics Department of the University of Nevada, Reno, Universita del Sannio, Cal Tech, California State University, Los Angeles, Univ of California - San Diego, UC Berkeley, Lawrence Livermore National Laboratory, Department of Physics & Astronomy, University of California, Irvine 92617, Department of Chemistry and of Physics & Astronomy, University of California, Irvine 92617, SLAC National Laboratory, Humboldt State University, Physics Department, University of Nevada, Reno, Univ of California - Merced