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arXiv · 0910.3662

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

Masaaki Nakamura·Emil J. Bergholtz·Juha Suorsa
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Abstract

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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Masaaki Nakamura, Emil J. Bergholtz, Juha Suorsa. 2009-10-19. Link between the hierarchy of fractional quantum Hall states and Haldane's conjecture for quantum spin chains. https://doi.org/10.1103/physrevb.81.165102

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