  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, discrete symmetries of low-lying
excitations, and string order parameters, we demonstrate that the $\nu=1/3$
fractional quantum Hall state is adiabatically connected to both Haldane and
large-$D$ phases, and is characterized by a string order parameter which is
dual to the ordinary one. This result indicates a close relation between (a
generalized form of) the Haldane conjecture for spin chains and the fractional
quantum Hall effect.
