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Transcript
Link between the hierarchy of fractional quantum Hall states and Haldane’s conjecture for quantum spin chains Masaaki Nakamura Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan We study a strong coupling expansion of the ν = 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 ν = 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. [1] M. Nakamura, E. J. Bergholtz, J. Suorsa, arXiv:0910.3662
