Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2011-05-11
J. Phys.: Conf. Ser. 302, 012020 (2011)
Physics
Condensed Matter
Strongly Correlated Electrons
8 pages, 3 figures, to appear in Journal of Physics: Conference Series as proceedings of International Symposium "Nanoscience
Scientific paper
10.1088/1742-6596/302/1/012020
We discuss the relationship between the fractional quantum Hall effect in the vicinity of the thin-torus, a.k.a. Tao-Thouless (TT), limit and quantum spin chains. We argue that the energetics of fractional quantum Hall states in Jain sequence at filling fraction $\nu=p/(2p+1)$ (and $\nu=1-p/(2p+1)$) in the lowest Landau level is captured by S=1 spin chains with $p$ spins in the unit cell. These spin chains naturally arise at sub-leading order in $\e^{-2\pi^2/L_1^2}$ which serves as an expansion parameter away from the TT limit ($L_1\rightarrow 0$). We also corroborate earlier results on the smooth Fermi surface deformation of the gapless state at $\nu=1/2$, interpolating between a state described by a critical $S=1/2$ chain and the bulk.
Bergholtz Emil J.
Nakamura Masaaki
Wang Zheng-Yuan
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