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

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

2009-10-19

arxiv.org/abs/0910.3662v3

Phys. Rev. B 81, 165102 (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

8 pages, 9 figures

Scientific paper

10.1103/PhysRevB.81.165102

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.

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