Vortices and Fractons

TL;DR

This paper presents an experimentally feasible realization of fracton physics through superfluid vortices, revealing conserved quantities and their relation to scalar charge theories, with implications for vortex hydrodynamics and curved space phenomena.

Contribution

It introduces a simple experimental setup linking vortex dynamics to fracton theories and explores vortex behavior on curved surfaces, connecting condensed matter and fracton physics.

Findings

Vortices conserve dipole and quadrupole moments, relating to scalar charge theories.

Vortex hydrodynamics also conserves these moments in large vortex limits.

Vortex motion on curved surfaces matches fracton behavior, enabling experimental studies.

Abstract

We discuss a simple and experimentally available realization of fracton physics. We note that superfluid vortices form a Hamiltonian system that conserves total dipole moment and trace of the quadrupole moment of vorticity; thereby establishing a relation to a traceless scalar charge theory in two spatial dimensions. Next we consider the limit where the number of vortices is large and show that emergent vortex hydrodynamics also conserves these moments. Finally, we show the motion of vortices and of fractons on curved surfaces agree, thereby opening a route to experimental study of the interplay between fracton physics and curved space. Our conclusions also apply to charged particles in strong magnetic field.