Massive Higher-Spin Fields in the Fractional Quantum Hall Effect

TL;DR

This paper explores the emergence of massive higher-spin fields in fractional quantum Hall systems, extending the understanding of geometric and order parameter descriptions beyond spin-2 to higher spins.

Contribution

It introduces a framework for describing non-relativistic massive chiral higher-spin fields in fractional quantum Hall phases using higher-rank tensors and derives their dynamics from relativistic theories.

Findings

Higher-spin modes naturally emerge in p-atic Hall phases.

Effective higher-spin Schroedinger actions describe these modes.

Relativistic higher-spin theories reduce to non-relativistic forms in 2+1 dimensions.

Abstract

Incompressibility plays a key role in the geometric description of fractional quantum Hall fluids. It is naturally related to quantum area-preserving diffeomorphisms and the underlying Girvin-MacDonald-Plazman algebra, which gives rise to an emergent non-relativistic massive spin-2 mode propagating in the bulk. The corresponding metric tensor can be identified with a nematic order parameter for the bulk states. In the linearised regime with a flat background, it has been shown that this mode can be described by a spin-2 Schroedinger action. However, quantum area-preserving diffeomorphisms also suggest the existence of higher-spin modes that cannot be described through nematic fractional quantum Hall states. Here, we consider p-atic Hall phases, in which the corresponding p-atic order parameters are related to higher-rank symmetric tensors. We then show that in this framework, non-relativistic massive chiral higher-spin fields naturally emerge and that their dynamics is described by higher-spin Schroedinger actions. We finally show that these effective actions can be derived from relativistic massive higher-spin theories in 2+1 dimensions after taking a non-relativistic limit.