Symmetry-Enriched Fracton Phases from Supersolid Duality

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 superhexatic 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.

Figure 1

A schematic phase diagram illustrating phases derived from the supersolid [a $U(1)$-symmetry broken fracton phase, $F$]. Upon condensation of appropriate defects, bosons can transition to a commensurate crystal [a $U(1)$-symmetric fracton phase, $F_{U(1)}$], superhexatic, or superfluid phase. Note that $U(1)$-symmetric liquid and hexatic phases are forbidden at zero temperature.

Figure 2

A disclination quadrupole, constructed as a bound state of two equal and opposite dislocations with Burgers vectors $\mathbf{b}$ and $-\mathbf{b}$, carries a unit of vacancy number, as can be seen by the deficiency of a single atom in the middle of the configuration.

Figure 3

(a) Fracton motion is forbidden as it requires emission of a conserved dipole. (b) Longitudinal dipole motion (dislocation climb) is forbidden as it requires emission of a linear quadrupole carrying conserved vacancy or interstitial number, corresponding to local compression of the crystal, i.e., a vacancy defect. (c) Transverse dipole motion (dislocation glide) is allowed as it creates a square quadrupole, corresponding to local shear.