Quasihole condensates in quantum Hall liquids

TL;DR

This paper introduces a formalism for describing quasihole condensates in quantum Hall liquids, extending conformal field theory to a broader hierarchy of states, including non-Abelian types, with explicit constructions at specific filling fractions.

Contribution

It develops a new formalism for quasihole condensates that generalizes existing models to include non-Abelian hierarchical states and provides explicit examples at certain filling fractions.

Findings

Constructed the level-two quasihole condensate at filling fraction 2/3.

Built two level-three states at 5/13 and 5/7 from quasielectron and quasihole condensates.

Extended conformal field theory approach to full hierarchy of quantum Hall states.

Abstract

We develop a formalism to describe quasihole condensates in quantum Hall liquids and thereby extend the conformal field theory approach to the full hierarchy of spin-polarized Abelian states, and to several classes of non-Abelian hierarchical states. Most previously proposed spin-polarized quantum Hall wave functions appear as special cases. In this paper we explain the physical motivations for the approach, and exemplify it by explicitly constructing the level-two quasihole condensate state at filling fraction 2/3, and the two level-three states at 5/13 and 5/7 which are built from combinations of quasielectron and quasihole condensates.