Projective Construction of Non-Abelian Quantum Hall Liquids

TL;DR

This paper introduces a projective construction method to generate and analyze non-Abelian quantum Hall states, including the Pfaffian state, enabling calculation of their bulk and edge theories and ground state degeneracies.

Contribution

It presents a new generalized parton construction for non-Abelian quantum Hall states, providing tools to derive their effective theories and physical properties.

Findings

Constructed non-Abelian QH states including Pfaffian at ν=1/2

Calculated bulk and edge effective theories for these states

Determined ground state degeneracy on torus

Abstract

Using projective construction, a generalized parton construction, we construct many non-Abelian quantum Hall (QH) states, which include the Pfaffian state at filling fraction $\nu=1/2$. The projective construction allows us to calculate the bulk and the edge effective theory for the constructed QH state. We illustrate how to use the bulk effective theory to calculate the ground state degeneracy of non-Abelian QH liquids on torus. We point out that the full description of the effective theory requires both the effective Lagrangian and the definition of electron operators. The latter generates all physical states and defines the gauge structure of the theory.