Stable Hierarchical Quantum Hall Fluids as W-(1 + infinity) Minimal Models

TL;DR

This paper develops a new hierarchical model for quantum Hall fluids using W-infinity minimal models, revealing non-Abelian excitations and aligning with experimental data, independent of Jain's approach.

Contribution

It introduces W-infinity minimal models for quantum Hall fluids, providing a novel hierarchical framework with non-Abelian excitations, matching experimental observations.

Findings

W-infinity minimal models match experimental fractional conductivities

Discovery of non-Abelian neutral excitations with SU(m) quantum numbers

A new hierarchical construction independent of Jain's approach

Abstract

In this paper, we pursue our analysis of the W-infinity symmetry of the low-energy edge excitations of incompressible quantum Hall fluids. These excitations are described by (1+1)-dimensional effective field theories, which are built by representations of the W-infinity algebra. Generic W-infinity theories predict many more fluids than the few, stable ones found in experiments. Here we identify a particular class of W-infinity theories, the minimal models, which are made of degenerate representations only - a familiar construction in conformal field theory. The W-infinity minimal models exist for specific values of the fractional conductivity, which nicely fit the experimental data and match the results of the Jain hierarchy of quantum Hall fluids. We thus obtain a new hierarchical construction, which is based uniquely on the concept of quantum incompressible fluid and is independent of Jain's approach and hypotheses. Furthermore, a surprising non-Abelian structure is found in the W-infinity minimal models: they possess neutral quark-like excitations with SU(m) quantum numbers and non-Abelian fractional statistics. The physical electron is made of anyon and quark excitations. We discuss some properties of these neutral excitations which could be seen in experiments and numerical simulations.