Link between the hierarchy of fractional quantum Hall states and Haldane's conjecture for quantum spin chains

Abstract

We study a strong coupling expansion of the $\nu =1/3$ fractional quantum Hall state away from the Tao-Thouless limit and show that the leading quantum fluctuations lead to an effective spin-1 Hamiltonian that lacks parity symmetry. By analyzing the energetics, discrete symmetries of low-lying excitations, and string order parameters, we demonstrate that the $\nu =1/3$ fractional quantum Hall state is adiabatically connected to both Haldane and large-$D$ phases, and is characterized by a string order parameter which is dual to the ordinary one. This result indicates a close relation between (a generalized form of) the Haldane conjecture for spin chains and the fractional quantum Hall effect.

8 pages, 9 figures

References in corpus (11)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Hidden order in 1D Bose 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
• One-Dimensional Theory of the Quantum Hall System
• Microscopic theory of the quantum Hall hierarchy
• Symmetry breaking in Laughlin's state on a cylinder
• Spin chain description of rotating bosons at $\nu =1$
• Quantum Hall Circle

Cited by in corpus (11)

• Symmetry protection of topological order in one-dimensional quantum spin systems
• Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands
• Exactly Solvable Fermion Chain Describing a $\nu =1/3$ Fractional Quantum Hall State
• Devil's staircases in synthetic dimensions and gauge fields
• Effective spin chains for fractional quantum Hall states
• Spin-chain description of fractional quantum Hall states in the Jain series
• Bosonic integer quantum Hall effect as topological pumping
• Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation
• Extraction of topological information in Tomonaga-Luttinger liquids
• Fractional topological insulator precursors in spin-orbit fermion ladders
• Excitation and tunneling spectra of a fractional quantum Hall system in the thin cylinder limit