Two-dimensional quantum liquids from interacting non-Abelian anyons

TL;DR

This paper demonstrates that interactions among non-Abelian anyons in two dimensions lead to a unique collective ground state, potentially forming a new gapped quantum liquid within the original quantum Hall state.

Contribution

It reveals how anyonic interactions in 2D can induce a transition to a novel gapped quantum liquid, advancing understanding of non-Abelian quantum Hall states.

Findings

Interactions lift degeneracy among non-Abelian anyons

A unique collective ground state emerges in 2D systems

Potential formation of a new gapped quantum liquid

Abstract

A set of localized, non-Abelian anyons - such as vortices in a p_x + i p_y superconductor or quasiholes in certain quantum Hall states - gives rise to a macroscopic degeneracy. Such a degeneracy is split in the presence of interactions between the anyons. Here we show that in two spatial dimensions this splitting selects a unique collective state as ground state of the interacting many-body system. This collective state can be a novel gapped quantum liquid nucleated inside the original parent liquid (of which the anyons are excitations). This physics is of relevance for any quantum Hall plateau realizing a non-Abelian quantum Hall state when moving off the center of the plateau.