Edge states of fractonic systems

This talk explores the nature of edge states in fractonic systems, revealing the connections between their characteristics with the bulk transport properties, accounting for quantum statistics of bulk excitations. The Chern-Simons theory of second-rank tensor gauge fields, parameterized by an integer level k introduced here, hosts a hierarchy of bulk excitations that include immobile point charges, transversely mobile dipoles and fully mobile quadrupoles. We show that the only combination of point excitations that produces a nontrivial statistical phase is a point quadrupole braiding around a point fracton charge. Exploring the cancellation of the gauge anomaly in a system with an edge, we show that two distinct types of edge excitations emerge. The current algebra of these excitations derived here reveals that the first type is a fractonic edge mode with immobile charges and longitudinal dipoles, while the second one is a non-fractonic mode with mobile transverse dipoles. We employ a renormalization group analysis to study the stability of edge modes against edge-to-edge tunneling and show it is a relevant perturbation, leading to edge reconstruction in fractonic systems. Our analysis offers ways to characterize a fractonic bulk by the study of edge dynamics.