Invariant structure of the hierarchy theory of fractional quantum Hall states with spin

TL;DR

This paper explores the invariant structures in the hierarchy theory of fractional quantum Hall states with spin, generalizing lattice descriptions to include spin-charge decomposition and SU(2) symmetry considerations.

Contribution

It introduces a generalized lattice framework for abelian fractional quantum Hall systems with spin, incorporating SU(2) invariance and spin-charge lattice structures.

Findings

Existence of a spin and charge lattice for systems with spin.

Multiple SU(2) symmetries in the spin-singlet hierarchy.

A description of spin-charge gluing via lattice theory.

Abstract

We describe the invariant structure common to abelian fractional quantum Hall systems with spin. It appears in a generalization of the lattice description of the polarized hierarchy that encompasses both partially polarized and unpolarized ground state systems. We formulate, using the spin-charge decomposition, conditions that should be satisfied so that the description is SU(2) invariant. In the case of the spin- singlet hierarchy construction, we find that there are as many SU(2) symmetries as there are levels in the construction. We show the existence of a spin and charge lattice for the systems with spin. The ``gluing'' of the charge and spin degrees of freedom in their bulk is described by the gluing theory of lattices.