Link between the hierarchy of fractional quantum Hall states and Haldane's conjecture for quantum spin chains

We study a strong coupling expansion of the $\nu=1/3$ fractional quantum Hall state away from the Tao-Thouless limit and show that the leading quantum fluctuations lead to an effective spin-1 Hamiltonian that lacks parity symmetry. By analyzing the energetics and discrete symmetries of low-lying excitations, we demonstrate that the $\nu=1/3$ fractional quantum Hall state is adiabatically connected to both Haldane and large-$D$ phases. This result indicates a close relation between the Haldane conjecture for spin chains and the fractional quantum Hall effect.