Symmetry Enriched Fracton Phases from Supersolid Duality

TL;DR

This paper develops a duality framework combining elasticity, boson-vortex duality, and supersolid order to describe fracton phases with both crystalline and superfluid properties, revealing new phase transitions and gauge dualities.

Contribution

It introduces a hybrid vector-tensor gauge dual of a supersolid that captures fracton behavior and superfluidity, advancing understanding of symmetry-enriched fracton phases.

Findings

Fracton states with full dipole mobility are described by a new gauge dual.

Phase transitions between distinct fracton phases are characterized by vortex condensation.

U(1)-symmetric phases are suppressed at zero temperature without crystalline order.

Abstract

Motivated by the recently established duality between elasticity of crystals and a fracton tensor gauge theory, we combine it with boson-vortex duality, to explicitly account for bosonic statistics of the underlying atoms. We thereby derive a hybrid vector-tensor gauge dual of a supersolid, which features both crystalline and superfluid order. The gauge dual describes a fracton state of matter with full dipole mobility endowed by the superfluid order, as governed by "mutual" axion electrodynamics between the fracton and vortex sectors of the theory, with an associated generalized Witten effect. Vortex condensation restores U(1) symmetry, confines dipoles to be subdimensional (recovering the dislocation glide constraint of a commensurate quantum crystal), and drives a phase transition between two distinct fracton phases. Meanwhile, condensation of elementary fracton dipoles and charges, respectively, provide a gauge dual description of the super-hexatic and ordinary superfluid. Consistent with conventional wisdom, in the absence of crystalline order, U(1)-symmetric phases are prohibited at zero temperature via a mechanism akin to deconfined quantum criticality.