A general approach to quantum Hall hierarchies

TL;DR

This paper develops a comprehensive formalism for constructing and analyzing quantum Hall hierarchy states, including abelian and non-abelian types, connecting wave functions, conformal field theory, and edge physics.

Contribution

It introduces a universal method to explicitly construct ground and quasiparticle wave functions for hierarchical quantum Hall states, extending previous formalisms.

Findings

Constructed explicit wave functions for abelian hierarchy states.

Connected hierarchical states to rational conformal field theory structures.

Validated wave functions against known results in the thin torus limit.

Abstract

The abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-abelian states emanating from the {\nu} = 5/2 Moore-Read state in the second Landau level. Extending a recently developed formalism for hierarchical quasihole condensation, we present a theory that allows for the explicit construction of the ground state wave function, as well as its quasiparticle excitations, for any state based on the abelian hierarchy. We relate our construction to structures in rational conformal field theory and stress the importance of using coherent state wave functions which allows us to formulate an extension of the bulk - edge correspondence that was conjectured by Moore and Read. Finally, we study the proposed ground state wave functions in the limiting geometry of a thin torus and argue that they coincide with the known exact results.