Construction of a series of new $\nu=2/5$ fractional quantum Hall wave functions by conformal field theory

TL;DR

This paper constructs new fractional quantum Hall wave functions at filling factor 2/5 using conformal field theory, demonstrating they maintain lowest Landau level projection and share topological properties with Jain states.

Contribution

It introduces a series of 2/5 fractional quantum Hall wave functions derived from conformal field theory that preserve LLL projection, unlike some Jain states, and establishes conditions for their topological properties.

Findings

CFT-based wave functions stay in LLL after projection

They share topological properties with Jain composite fermion states

Necessary conditions for nonvanishing LLL projection are proven

Abstract

In this paper, a series of $\nu=2/5$ fractional quantum Hall wave functions are constructed from conformal field theory(CFT). They share the same topological properties with states constructed by Jain's composite fermion approach. Upon exact lowest Landau level(LLL) projection, some of Jain composite fermion states would not survive if constraints on Landau level indices given in the appendices of this paper were not satisfied. By contrast, states constructed from CFT always stay in LLL. These states are characterized by different topological shifts and multibody relative angular momenta. As a by-product, in the appendices we prove the necessary conditions for general $ \nu=p/(2p+1) $ composite fermion states to have nonvanishing LLL projection.