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

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.

21 pages, LaTex, Submitted to Phys. Rev. B

References in corpus (2)

• Edge excitations of paired fractional quantum Hall states
• Quantum Hall States of High Symmetry

Cited by in corpus (8)

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• Separation of spin and charge in paired spin-singlet quantum Hall states
• SU(N) fractional quantum Hall effects in topological flat bands
• Effective field theory for the bulk and edge states of quantum Hall states in unpolarized single layer and bilayer systems
• Cooper pair tunneling in junctions of singlet quantum Hall states and superconductors
• Modified Coulomb gas construction of quantum Hall states from non-unitary conformal field theories
• Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU($N$) symmetry