Entanglement in the quantum Hall fluid of dipoles

TL;DR

This paper analyzes a gapped fractonic order model in 2+1 dimensions, revealing its entanglement structure, edge excitations, and connections to quantum Hall physics, including fractionalized dipoles and topological entanglement.

Contribution

It introduces a novel interpretation of fractonic order as a dipole condensate with fractionalized excitations, linking it to quantum Hall-like topological features.

Findings

Ground-state entanglement entropy computed with topological correction

Identification of gapless Lifshitz-type edge modes

Interpretation of the vacuum as a dipole condensate with anyonic excitations

Abstract

We revisit a model for gapped fractonic order in (2+1) dimensions (a symmetric-traceless tensor gauge theory with conservation of dipole and trace-quadrupole moments described in \cite{Prem:2017kxc}) and compute its ground-state entanglement entropy on $\mathbb R^2$. Along the way, we quantize the theory on open subsets of $\mathbb R^2$ which gives rise to gapless edge excitations that are Lifshitz-type scalar theories. We additionally explore varieties of gauge-invariant extended operators and rephrase the fractonic physics in terms of the local deformability of these operators. We explore similarities of this model to the effective field theories describing quantum Hall fluids: in particular, quantization of dipole moments through a novel compact symmetry leads us to interpret the vacuum of this theory as a dipole condensate atop of which dipoles with fractionalized moments appear as quasi-particle excitations with Abelian anyonic statistics. This interpretation is reflected in the subleading "topological entanglement" correction to the entanglement entropy. We extend this result to a series of models with conserved multipole moments.