Fractons on the edge

TL;DR

This paper develops a theory of edge excitations in two-dimensional fractonic systems, revealing unique braiding phases, gapless edge modes, and their relation to bulk properties, with implications for boundary dynamics.

Contribution

It introduces a novel framework for understanding edge excitations in fractonic phases, including a current algebra and analysis of edge tunneling effects.

Findings

Quantized braiding phases occur only in specific quadrupole and dipole braiding scenarios.

Two types of gapless edge modes are identified: fractonic and non-fractonic.

Edge tunneling can deform edge modes, indicating boundary flexibility.

Abstract

We develop a theory of edge excitations of fractonic systems in two dimensions, and elucidate their connections to bulk transport properties and quantum statistics of bulk excitations. The system we consider has immobile point charges, dipoles constrained to move only along lines perpendicular to their moment, and freely mobile quadrupoles and higher multipoles, realizing a bulk fractonic analog of fractional quantum Hall phases. We demonstrate that a quantized braiding phase between two bulk excitations is obtained only in two cases: when a point quadrupole braids around an immobile point charge, or when two non-orthogonal point dipoles braid with one another. The presence of a boundary edge in the system entails $\textit{two}$ types of gapless edge excitation modes, one that is fractonic with immobile charges and longitudinal dipoles, and a second non-fractonic mode consisting of transverse dipoles. We derive a novel current algebra of the fractonic edge modes. Further, investigating the effect of local edge-to-edge tunneling on these modes, we find that such a process is a relevant perturbation suggesting the possibility of edge deformation.