Spin Singlet Quantum Hall Effect and Nonabelian Landau-Ginzburg Theory

TL;DR

This paper develops a field-theoretic model for the Spin Singlet Quantum Hall Effect, revealing a nonabelian Landau-Ginzburg theory with $SU(2)$ gauge symmetry and spin-charge separation.

Contribution

It introduces a novel $SU(2)_{k=1}$ Chern-Simons Landau-Ginzburg framework for SQHE, connecting wave functions, spin liquids, and nonabelian gauge potentials.

Findings

Wave function factorization into charged and neutral components

Presence of $SU(2)$ gauge potential due to spin rigidity

Construction of coherent states demonstrating nonabelian gauge structure

Abstract

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-$\12$ semions. We introduce field-theoretic model in which the electron operators are factorized in terms of charged spinless semions (holons) and neutral spin-$\12$ 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.