Effective spin chains for fractional quantum Hall states

TL;DR

This paper reviews how effective spin chain models can describe fractional quantum Hall states near the thin-torus limit, revealing differences between bosonic and fermionic states and connecting to entanglement studies.

Contribution

It clarifies the distinction between bosonic and fermionic FQH states in effective spin chain models and explores their relation to the Haldane-Shastry chain and entanglement.

Findings

Effective spin chains capture FQH properties near the thin-torus limit.

Differences between bosonic and fermionic FQH states are elucidated.

Connection established between the Haldane-Shastry chain and QH circle limit.

Abstract

Fractional quantum Hall (FQH) states are topologically ordered which indicates that their essential properties are insensitive to smooth deformations of the manifold on which they are studied. Their microscopic Hamiltonian description, however, strongly depends on geometrical details. Recent work has shown how this dependence can be exploited to generate effective models that are both interesting in their own right and also provide further insight into the quantum Hall system. We review and expand on recent efforts to understand the FQH system close to the solvable thin-torus limit in terms of effective spin chains. In particular, we clarify how the difference between the bosonic and fermionic FQH states, which is not apparent in the thin-torus limit, can be seen at this level. Additionally, we discuss the relation of the Haldane-Shastry chain to the so-called QH circle limit and comment on its significance to recent entanglement studies.