Spin Singlet Quantum Hall Effect and Nonabelian Landau-Ginzburg Theory

In this paper we present a theory of Singlet Quantum Hall Effect (SQHE). We show that the Halperin-Haldane 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 spin-½ semions. We introduce field-theoretic model in which the electron operators are factorized in terms of charged spinless semions (holons) and neutral spin-½ semions (spinons). Broken time reversal symmetry and short ranged spin correlations lead to SU(2)k=1 Chern-Simons term in Landau-Ginzburg action for SQHE phase. We construct appropriate coherent states for SQHE phase and show the existence of SU(2) valued gauge potential. This potential appears as a result of “spin rigidity” of the ground state against any displacements of nodes of wave function from positions of the particles and reflects the nontrivial monodromy in the presence of these displacements. We argue that topological structure of SU(2)k=1 Chern-Simons theory unambiguously dictates semion statistics of spinons.