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

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 $\e^{-2π^2/L_1^2}$ which serves as an expansion parameter away from the TT limit ($L_1\to 0$). 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.

8 pages, 3 figures, to appear in Journal of Physics: Conference Series as proceedings of International Symposium "Nanoscience and Quantum Physics 2011" (nanoPHYS'11)

References in corpus (17)

• Non-Abelian Anyons and Topological Quantum Computation
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Quantum Hall system in Tao-Thouless limit
• Half-Filled Lowest Landau Level on a Thin Torus
• Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
• Quantum Hall physics in rotating Bose-Einstein condensates
• The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
• One-Dimensional Theory of the Quantum Hall System
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory
• Microscopic theory of the quantum Hall hierarchy
• Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
• Domain walls, fusion rules and conformal field theory in the quantum Hall regime
• Effective spin chains for fractional quantum Hall states
• Spin chain description of rotating bosons at $\nu =1$
• Quantum Hall Circle

Cited by in corpus (6)

• Quantum Many-body Scars in a Landau Level on a Thin Torus
• Composite Fermions on a Torus
• Spin-chain description of fractional quantum Hall states in the Jain series
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• Matrix-Product Ansatz for Excited States of Fractional Quantum Hall Systems
• Interband excitations in the 1D limit of two-band fractional Chern insulators