# Fractons on the edge

**Authors:** Bhandaru Phani Parasar, Yuval Gefen, Vijay B. Shenoy  
**arXiv:** [2411.19620](https://arxiv.org/abs/2411.19620)  
**Date:** 2024-11-29  
**Summary page:** https://www.summarizepaper.com/en/paper/2411.19620v1/

## Key points

- Edge excitations in fractonic systems in two dimensions have profound connections to bulk transport properties and quantum statistics of bulk excitations.
- The system consists of immobile point charges, dipoles moving along perpendicular lines, and freely mobile quadrupoles and higher multipoles, creating a bulk fractonic analog similar to fractional quantum Hall phases.
- A quantized braiding phase between bulk excitations occurs when a point quadrupole braids around an immobile point charge or when two non-orthogonal point dipoles engage in braiding.
- The presence of a boundary edge introduces two distinct types of gapless edge excitation modes: one with fractonic elements like immobile charges and longitudinal dipoles, and another with non-fractonic elements such as transverse dipoles.
- A novel current algebra governs the behavior of these fractonic edge modes.
- Local edge-to-edge tunneling processes impact these modes, hinting at potential edge deformation.
- The study draws upon existing research in topological quantum matter with symmetries, exploring diverse quantum-topological phases and instances of topological overprotection in clean systems.
- Topics like topological quantum glassiness, local stabilizer codes without string logical operators, dimensional hierarchies of quasiparticles from multipole interactions are touched upon.
- Allowed tunneling processes between edges involving longitudinal dipoles are discussed in detail.

## Summary

We explore the intricate realm of edge excitations in fractonic systems within two dimensions, shedding light on their profound connections to bulk transport properties and the quantum statistics of bulk excitations. The system under scrutiny comprises immobile point charges, dipoles constrained to motion along lines perpendicular to their moment, and freely mobile quadrupoles and higher multipoles. This setup materializes a bulk fractonic analog akin to fractional quantum Hall phases. Our investigation uncovers that a quantized braiding phase between two bulk excitations manifests solely in two scenarios: when a point quadrupole braids around an immobile point charge or when two non-orthogonal point dipoles engage in braiding. Notably, the presence of a boundary edge introduces not one but $\textit{two}$ distinct types of gapless edge excitation modes. One mode exhibits a fractonic nature characterized by immobile charges and longitudinal dipoles, while the other mode comprises non-fractonic elements such as transverse dipoles. Moreover, we derive a novel current algebra governing the behavior of these fractonic edge modes. By delving into the impact of local edge-to-edge tunneling on these modes, we uncover that such processes serve as relevant perturbations hinting at the potential for edge deformation. This exploration adds depth to our understanding of fractonic systems and their intriguing interplay between bulk and edge phenomena. Additionally, our study draws upon existing research in topological quantum matter with symmetries [6], highlighting the diverse zoo of quantum-topological phases [7] and instances of topological overprotection in strongly correlated clean systems [8]. We also touch upon topics like topological quantum glassiness [9], local stabilizer codes without string logical operators [10], and dimensional hierarchies of quasiparticles built from multipole interactions [11]. Furthermore, allowed tunneling processes between edges involving longitudinal dipoles are discussed in detail [12]. Overall, this comprehensive analysis enriches our comprehension of fractons on the edge and contributes valuable insights to the broader landscape of topological quantum phenomena.