Spin Singlet Quantum Hall Effect and Nonabelian Landau-Ginzburg Theory

TL;DR

This paper presents a field-theoretic model for the Spin Singlet Quantum Hall Effect, revealing the role of SU(2) Chern-Simons theory in describing semion statistics and the topological structure of the phase.

Contribution

It introduces a novel Landau-Ginzburg framework with an SU(2) gauge potential to explain nonabelian spinon statistics in the SQHE phase.

Findings

Wave function factorization into charged and neutral components.

Existence of SU(2) gauge potential due to spin rigidity.

Topological structure dictates semion statistics of spinons.

Abstract

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. We argue that topological structure of $SU(2)_{k=1}$ Chern-Simons theory unambiguously dictates {\it semion} statistics of spinons.