Particle Hole Symmetry Breaking In the Fractional Quantum Hall Effect at $\nu = \frac{5}{2}$

ORAL

Abstract

The fractional quantum Hall effect (FQHE) is widely studied because of its exotic topological phases. The FQHE at $\nu = \frac{5}{2}$ is interesting because it supports excitations of non-abelian quasiparticles. These non-abelian particles are one possible candidate for use as qubits in topological quantum computations. The leading theoretical description of the FQHE at $\nu = \frac{5}{2}$ is the Moore-Reed Pfaffian and its particle hole conjugate the anti-Pfaffian. The Pfaffian and the anti-Pfaffian are the exact ground states of a three body Hamiltonian ($H_3$) and its particle hole conjugate ($H^\prime_3$), respectively. The Pfaffian breaks particle hole symmetry (PHS) explicitly while the physical interaction (Coulomb) is largely PHS. We define a PHS Hamiltonian (H$_2$) and ask is PHS breaking necessary in order to produce a Pfaffian ground state? To answer, we study $H(\alpha)= (1-\alpha)H_3 + \alpha H_2$ and tune alpha from 0 to 1. We show that the ground and low energy states for $H_2$ and $H_3$ remain adiabatically connected. This adiabatic connection shows the low energy states for $H_2$ and $H_3$ are in the same universality class.

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Authors

  • William D. Hutzel

    Department of Physics and Astronomy, California State University Long Beach, Long Beach, California 90840, USA

  • C. Jennings

    Stanford University, None, none, Univ of California - Merced, Dr. Remeis-Sternwarte & ECAP, Universität Erlangen-Nürnberg, NASA GSFC, Lawrence Livermore Natl Lab, Lawrence Livermore National Laboratory, Goddard Space Flight Center-NASA, University of Nevada, Reno, Cal Poly - San Luis Obispo, Victoria University of Wellington, Wellington 6021, New Zealand, Penn State, Micron School of Materials Science & Engineering, Department of Physics, Boise State University, Autonomous University of Zacatecas, Micron School of Materials Science & Engineering, Boise State University, Naval Research Laboratory, Independent Researcher, Cornell University, UC Santa Cruz, Middle Georgia State University, University of California, Merced, Stanford University, California, Institute of Medical Biology, Singapore; Stanford University, California, University of California Merced, Kent State University, ORNL, UC Berkeley, LLNL, Physics, Hokkaido University, Japan, Physics, UC San Diego, Physics, California State University, Fresno, Department of Physics and Astronomy, California State University Long Beach, Long Beach, California 90840, USA, Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA, Department of Physics, Southern University of Science and Technology, Shenzen 518055, China, Virginia Tech, Sotera Defense Solutions, Inc., Univ of California - Santa Cruz, College of Staten Island, UC Irvine, Naval Research Laboratory, Washington, DC 20375, Virginia Tech, Blacksburg, VA 24061, University of California, Merced CA 95343

  • C. Jennings

    Stanford University, None, none, Univ of California - Merced, Dr. Remeis-Sternwarte & ECAP, Universität Erlangen-Nürnberg, NASA GSFC, Lawrence Livermore Natl Lab, Lawrence Livermore National Laboratory, Goddard Space Flight Center-NASA, University of Nevada, Reno, Cal Poly - San Luis Obispo, Victoria University of Wellington, Wellington 6021, New Zealand, Penn State, Micron School of Materials Science & Engineering, Department of Physics, Boise State University, Autonomous University of Zacatecas, Micron School of Materials Science & Engineering, Boise State University, Naval Research Laboratory, Independent Researcher, Cornell University, UC Santa Cruz, Middle Georgia State University, University of California, Merced, Stanford University, California, Institute of Medical Biology, Singapore; Stanford University, California, University of California Merced, Kent State University, ORNL, UC Berkeley, LLNL, Physics, Hokkaido University, Japan, Physics, UC San Diego, Physics, California State University, Fresno, Department of Physics and Astronomy, California State University Long Beach, Long Beach, California 90840, USA, Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA, Department of Physics, Southern University of Science and Technology, Shenzen 518055, China, Virginia Tech, Sotera Defense Solutions, Inc., Univ of California - Santa Cruz, College of Staten Island, UC Irvine, Naval Research Laboratory, Washington, DC 20375, Virginia Tech, Blacksburg, VA 24061, University of California, Merced CA 95343

  • C. Jennings

    Stanford University, None, none, Univ of California - Merced, Dr. Remeis-Sternwarte & ECAP, Universität Erlangen-Nürnberg, NASA GSFC, Lawrence Livermore Natl Lab, Lawrence Livermore National Laboratory, Goddard Space Flight Center-NASA, University of Nevada, Reno, Cal Poly - San Luis Obispo, Victoria University of Wellington, Wellington 6021, New Zealand, Penn State, Micron School of Materials Science & Engineering, Department of Physics, Boise State University, Autonomous University of Zacatecas, Micron School of Materials Science & Engineering, Boise State University, Naval Research Laboratory, Independent Researcher, Cornell University, UC Santa Cruz, Middle Georgia State University, University of California, Merced, Stanford University, California, Institute of Medical Biology, Singapore; Stanford University, California, University of California Merced, Kent State University, ORNL, UC Berkeley, LLNL, Physics, Hokkaido University, Japan, Physics, UC San Diego, Physics, California State University, Fresno, Department of Physics and Astronomy, California State University Long Beach, Long Beach, California 90840, USA, Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA, Department of Physics, Southern University of Science and Technology, Shenzen 518055, China, Virginia Tech, Sotera Defense Solutions, Inc., Univ of California - Santa Cruz, College of Staten Island, UC Irvine, Naval Research Laboratory, Washington, DC 20375, Virginia Tech, Blacksburg, VA 24061, University of California, Merced CA 95343

  • C. Jennings

    Stanford University, None, none, Univ of California - Merced, Dr. Remeis-Sternwarte & ECAP, Universität Erlangen-Nürnberg, NASA GSFC, Lawrence Livermore Natl Lab, Lawrence Livermore National Laboratory, Goddard Space Flight Center-NASA, University of Nevada, Reno, Cal Poly - San Luis Obispo, Victoria University of Wellington, Wellington 6021, New Zealand, Penn State, Micron School of Materials Science & Engineering, Department of Physics, Boise State University, Autonomous University of Zacatecas, Micron School of Materials Science & Engineering, Boise State University, Naval Research Laboratory, Independent Researcher, Cornell University, UC Santa Cruz, Middle Georgia State University, University of California, Merced, Stanford University, California, Institute of Medical Biology, Singapore; Stanford University, California, University of California Merced, Kent State University, ORNL, UC Berkeley, LLNL, Physics, Hokkaido University, Japan, Physics, UC San Diego, Physics, California State University, Fresno, Department of Physics and Astronomy, California State University Long Beach, Long Beach, California 90840, USA, Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA, Department of Physics, Southern University of Science and Technology, Shenzen 518055, China, Virginia Tech, Sotera Defense Solutions, Inc., Univ of California - Santa Cruz, College of Staten Island, UC Irvine, Naval Research Laboratory, Washington, DC 20375, Virginia Tech, Blacksburg, VA 24061, University of California, Merced CA 95343

  • C. Jennings

    Stanford University, None, none, Univ of California - Merced, Dr. Remeis-Sternwarte & ECAP, Universität Erlangen-Nürnberg, NASA GSFC, Lawrence Livermore Natl Lab, Lawrence Livermore National Laboratory, Goddard Space Flight Center-NASA, University of Nevada, Reno, Cal Poly - San Luis Obispo, Victoria University of Wellington, Wellington 6021, New Zealand, Penn State, Micron School of Materials Science & Engineering, Department of Physics, Boise State University, Autonomous University of Zacatecas, Micron School of Materials Science & Engineering, Boise State University, Naval Research Laboratory, Independent Researcher, Cornell University, UC Santa Cruz, Middle Georgia State University, University of California, Merced, Stanford University, California, Institute of Medical Biology, Singapore; Stanford University, California, University of California Merced, Kent State University, ORNL, UC Berkeley, LLNL, Physics, Hokkaido University, Japan, Physics, UC San Diego, Physics, California State University, Fresno, Department of Physics and Astronomy, California State University Long Beach, Long Beach, California 90840, USA, Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA, Department of Physics, Southern University of Science and Technology, Shenzen 518055, China, Virginia Tech, Sotera Defense Solutions, Inc., Univ of California - Santa Cruz, College of Staten Island, UC Irvine, Naval Research Laboratory, Washington, DC 20375, Virginia Tech, Blacksburg, VA 24061, University of California, Merced CA 95343

  • C. Jennings

    Stanford University, None, none, Univ of California - Merced, Dr. Remeis-Sternwarte & ECAP, Universität Erlangen-Nürnberg, NASA GSFC, Lawrence Livermore Natl Lab, Lawrence Livermore National Laboratory, Goddard Space Flight Center-NASA, University of Nevada, Reno, Cal Poly - San Luis Obispo, Victoria University of Wellington, Wellington 6021, New Zealand, Penn State, Micron School of Materials Science & Engineering, Department of Physics, Boise State University, Autonomous University of Zacatecas, Micron School of Materials Science & Engineering, Boise State University, Naval Research Laboratory, Independent Researcher, Cornell University, UC Santa Cruz, Middle Georgia State University, University of California, Merced, Stanford University, California, Institute of Medical Biology, Singapore; Stanford University, California, University of California Merced, Kent State University, ORNL, UC Berkeley, LLNL, Physics, Hokkaido University, Japan, Physics, UC San Diego, Physics, California State University, Fresno, Department of Physics and Astronomy, California State University Long Beach, Long Beach, California 90840, USA, Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA, Department of Physics, Southern University of Science and Technology, Shenzen 518055, China, Virginia Tech, Sotera Defense Solutions, Inc., Univ of California - Santa Cruz, College of Staten Island, UC Irvine, Naval Research Laboratory, Washington, DC 20375, Virginia Tech, Blacksburg, VA 24061, University of California, Merced CA 95343