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We discuss the relationship between the fractional quantum Hall effect in thevicinity of the thin-torus, a.k.a. Tao-Thouless (TT), limit and quantum spinchains. We argue that the energetics of fractional quantum Hall states in Jainsequence at filling fraction $\nu=p/(2p+1)$ (and $\nu=1-p/(2p+1)$) in thelowest Landau level is captured by S=1 spin chains with $p$ spins in the unitcell. 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 TTlimit ($L_1\rightarrow 0$). We also corroborate earlier results on the smoothFermi surface deformation of the gapless state at $\nu=1/2$, interpolatingbetween a state described by a critical $S=1/2$ chain and the bulk.

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