Spinless basis for spin-singlet FQH states

TL;DR

This paper explores a novel spinless basis approach to describe SU(M)-singlet fractional quantum Hall states, connecting q-deformed Laughlin states and the Yangian Gelfand-Zetlin basis, with implications for understanding their structure.

Contribution

It introduces a new spinless basis framework for SU(M)-singlet FQH states, linking q-deformation, root of unity limits, and the Yangian basis.

Findings

Derived the SU(M)-singlet Halperin state via q-deformation of Laughlin state.

Analyzed the squeezing rule for SU(M) states in the spinless basis.

Connected the basis to the spin Calogero-Sutherland model.

Abstract

We investigate an alternative description of the SU(M)-singlet FQH state by using the spinless basis. The SU(M)-singlet Halperin state is obtained via the q-deformation of the Laughlin state and its root of unity limit, by applying the Yangian Gelfand-Zetlin basis for the spin Calogero-Sutherland model. The squeezing rule for the SU(M) state is also investigated in terms of the spinless basis.