Spin chain description of rotating bosons at $\nu =1$

Abstract

We consider bosons at Landau level filling $\nu =1$ on a thin torus. In analogy with previous work on fermions at filling $\nu =1/2$, we map the low-energy sector onto a spin-1/2 chain. While the fermionic system may realize the gapless XY-phase, we show that typically this does not happen for the bosonic system. Instead, both delta function and Coulomb interaction lead to gapped phases in the bosonic system, and in particular we identify a phase corresponding to the non-abelian Moore-Read state. In the spin language, the hamiltonian is dominated by a ferromagnetic next-nearest neighbor interaction, which leads to a description consistent with the non-trivial degeneracies of the ground and excited states of this phase of matter. In addition we comment on the similarities and differences of the two systems mentioned above and fermions at $\nu =5/2$.

Published. 19 pages, 4 figures

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Cited by in corpus (10)

• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Abelian and non-Abelian statistics in the coherent state representation
• Entanglement spectrum: Identification of the transition from vortex-liquid to vortex-lattice state in a weakly interacting rotating Bose-Einstein condensate
• Effective spin chains for fractional quantum Hall states
• Bosonic integer quantum Hall effect as topological pumping
• Link between the hierarchy of fractional quantum Hall states and Haldane's conjecture for quantum spin chains
• Spin chain description of rotating bosons at $\nu =1$
• Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation
• Gaffnian holonomy through the coherent state method