Exactly Solvable Fermion Chain Describing a $\nu =1/3$ Fractional Quantum Hall State

Abstract

We introduce an exactly solvable fermion chain that describes a $\nu =1/3$ fractional quantum Hall (FQH) state beyond the thin-torus limit. The ground state of our model is shown to be unique for each center of mass sector, and it has a matrix product representation that enables us to exactly calculate order parameters, correlation functions, and entanglement spectra. The ground state of our model shows striking similarities with the BCS wave functions and quantum spin-1 chains. Using the variational method with matrix product ansatz, we analytically calculate excitation gaps and vanishing of the compressibility expected in the FQH state. We also show that the above results can be related to a $\nu =1/2$ bosonic FQH state.

5 pages. 3 figures, the final version, a related paper arXiv:1206.3071

References in corpus (12)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
• Rise and fall of hidden string order of lattice bosons
• Quantum Hall system in Tao-Thouless limit
• Half-Filled Lowest Landau Level on a Thin Torus
• Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect
• One-Dimensional Theory of the Quantum Hall System
• Effective spin chains for fractional quantum Hall states
• Jastrow-Correlated Wavefunctions for Flat-Band Lattices

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