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

TL;DR

This paper explores the connection between fractional quantum Hall states near the Tao-Thouless limit and quantum spin chains, revealing how spin chain models capture the energetics and Fermi surface deformation of these states.

Contribution

It introduces a spin chain framework to describe fractional quantum Hall states near the TT limit, providing a new perspective on their energetics and Fermi surface behavior.

Findings

Fractional quantum Hall states are modeled by S=1 spin chains with p spins per unit cell.

The spin chain description emerges at sub-leading order in an expansion parameter away from the TT limit.

The Fermi surface deformation at ν=1/2 is smoothly interpolated between critical S=1/2 chain and bulk states.

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 $\nu=p/(2p+1)$ (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.