Singlet quantum Hall effect and ChernSimons theories
Abstract
In this paper, we present a theory of the singlet quantum Hall effect (SQHE). We show that the HalperinHaldane SQHE wave function can be written in the form of a product of a wave function for charged semions in a magnetic field and a wave function for the chiral spin liquid of neutral spin1/2 semions. We introduce a fieldtheoretic model in which the electron operators are factorized in terms of charged spinless semions (holons) and neutral spin1/2 semions (spinons). Holons and spinons are described in terms of a spinless charged fermion field coupled to U(1) (charge) ChernSimons gauge field and a spin1/2 neutral fermion coupled to SU(2) (spin) ChernSimons gauge fields, respectively. Only the holons couple to the magnetic field. The physics that we find agrees with the results obtained using the HaldaneHalperin wave function: the spectrum of excitations has a gap and the quantum Hall conductance σ_{xy} equals ν/2π, where ν is the filling fraction. The entire spectrum of physical states is shown to factorize into a charge and a spin contribution. Our picture makes the SU(2) spin symmetry manifest. The spin sector of the wave function is shown to behave like a conformal block of primary fields of the SU(2) WessZuminoWitten model. The conformal dimensions of primary fields unambiguously dictates the semion statistics of the spinons. We find a generalization of the Fock cyclic condition for singlet semion wave functions.
 Publication:

Physical Review B
 Pub Date:
 May 1991
 DOI:
 10.1103/PhysRevB.43.10622
 Bibcode:
 1991PhRvB..4310622B
 Keywords:

 73.20.Dx;
 11.15.q;
 75.10.Jm;
 74.65.+n;
 Gauge field theories;
 Quantized spin models