Fractonic gauge theory of smectics

TL;DR

This paper develops a dual gauge theory framework for 2D quantum smectics, revealing fractonic behavior of disclinations and connecting quantum and classical melting transitions through dualities and Higgs mechanisms.

Contribution

It introduces a novel dual coupled U(1) gauge theory for 2D quantum smectics, linking elasticity, fractons, and phase transitions via gauge dualities and Higgs transitions.

Findings

Disclinations in smectics behave as fractonic charges with restricted mobility.

The dual gauge theory describes quantum melting via dislocation proliferation.

Classical smectic melting is unstable to nematic at any nonzero temperature.

Abstract

Motivated by striped correlated quantum matter, and the recently developed duality between elasticity of a two-dimensional (2D) crystal and a gauge theory, we derive a dual coupled U(1) vector gauge theory for a two-dimensional (2D) quantum smectic, where the disclination is mapped onto the fractonic charge, that we demonstrate can only move transversely to smectic layers. This smectic gauge theory dual also emerges from a gauge dual of a quantum crystal after a Higgs transition corresponding to a single flavor of its dipole condensation, an anisotropic quantum melting via dislocation proliferation. A condensation of the second flavor of dislocations is described by another Higgs transition describing the smectic-to-nematic melting. We also utilize the electrostatic limit of this duality to formulate a melting of a 2D classical smectic in terms of a higher derivative sine- Gordon model, demonstrating its instability to a nematic at any nonzero temperature. Generalizing this classical duality to a 3D smectic, gives formulation of a 3D nematic-to-smectic transition in terms of an anisotropic Abelian-Higgs model.