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arXiv · 1105.2105

Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation

Masaaki Nakamura·Zheng-Yuan Wang·Emil J. Bergholtz
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Abstract

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 $ν=p/(2p+1)$ (and $ν=1-p/(2p+1)$) 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 $\e^{-2π^2/L_1^2}$ 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 $ν=1/2$, interpolating between a state described by a critical $S=1/2$ chain and the bulk.

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Masaaki Nakamura, Zheng-Yuan Wang, Emil J. Bergholtz. 2011-05-11. Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation. https://doi.org/10.1088/1742-6596%2F302%2F1%2F012020

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