Spin-singlet Gaffnian wave function for fractional quantum Hall systems

Simon C. Davenport, Eddy Ardonne, Nicolas Regnault, and Steven H. Simon
Phys. Rev. B 87, 045310 – Published 22 January 2013

Abstract

We characterize in detail a wave function conceivable in fractional quantum Hall systems where a spin or equivalent degree of freedom is present. This wave function combines the properties of two previously proposed quantum Hall wave functions, namely the non-Abelian spin-singlet state and the nonunitary Gaffnian wave function. This is a spin-singlet generalization of the spin-polarized Gaffnian, which we call the “spin-singlet Gaffnian” (SSG). In this paper we present evidence demonstrating that the SSG corresponds to the ground state of a certain local Hamiltonian, which we explicitly construct, and, further, we provide a relatively simple analytic expression for the unique ground-state wave functions, which we define as the zero energy eigenstates of that local Hamiltonian. In addition, we have determined a certain nonunitary, rational conformal field theory which provides an underlying description of the SSG and we thus conclude that the SSG is ungapped in the thermodynamic limit. In order to verify our construction, we implement two recently proposed techniques for the analysis of fractional quantum Hall trial states: The “spin dressed squeezing algorithm,” and the “generalized Pauli principle.”

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  • Received 8 November 2012

DOI:https://doi.org/10.1103/PhysRevB.87.045310

©2013 American Physical Society

Authors & Affiliations

Simon C. Davenport1, Eddy Ardonne2,3, Nicolas Regnault4,5, and Steven H. Simon1

  • 1Rudolf Peierls Centre for Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom
  • 2Nordita, Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
  • 3Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden
  • 4Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 5Laboratoire Pierre Aigrain, ENS and CNRS, 24 rue Lhomond, F-75005 Paris, France

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Issue

Vol. 87, Iss. 4 — 15 January 2013

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