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

TL;DR

This paper maps bosons at Landau level filling ν=1 on a thin torus to a spin chain, revealing gapped phases including a non-abelian Moore-Read state, contrasting with fermionic systems that may be gapless.

Contribution

It introduces a spin chain model for bosons at ν=1, identifying gapped phases and the non-abelian Moore-Read state, expanding understanding of bosonic quantum Hall systems.

Findings

Bosonic system exhibits gapped phases under delta and Coulomb interactions.

Identifies a phase corresponding to the non-abelian Moore-Read state.

Spin Hamiltonian dominated by ferromagnetic next-nearest neighbor interactions.

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 $\nu=5/2$.