Fractonic line excitations : an inroad from 3d elasticity theory

TL;DR

This paper introduces fractonic line excitations in 3D elasticity, showing their connection to gauge theories and lattice defects, with implications for melting transitions and quantum error correction.

Contribution

It establishes a novel link between fractonic line excitations and 3D elasticity theory, using gauge theories to describe restricted mobility of lattice defects.

Findings

Identification of fractonic line excitations as topological lattice defects

Mapping elasticity theory to rank-4 tensor gauge theory

Derivation of flux conservation laws restricting defect mobility

Abstract

We demonstrate the existence of a fundamentally new type of excitation, fractonic lines, which are line-like excitations with the restricted mobility properties of fractons. These excitations, described using an amalgamation of higher-form gauge theories with symmetric tensor gauge theories, see direct physical realization as the topological lattice defects of ordinary three-dimensional quantum crystals. Starting with the more familiar elasticity theory, we show how it maps onto a rank-4 tensor gauge theory, with phonons corresponding to gapless gauge modes and disclination defects corresponding to line-like charges. We derive flux conservation laws which lock these line-like excitations in place, analogous to the higher moment charge conservation laws of fracton theories. This way of encoding mobility restrictions of lattice defects could shed light on melting transitions in three dimensions. This new type of extended object may also be a useful tool in the search for improved quantum error-correcting codes in three dimensions.