Symmetry-Enriched Fracton Phases from Supersolid Duality

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. arXiv:1808.05616v2 [cond-mat.str-el]

Fracton phases of matter

“…If atom number were not conserved, then a dislocation would be able to move freely in all directions. This indicates that the mobility restrictions on dislocations are enforced by the presence of an extra global U (1) symmetry in a manifestation of "symmetry-protected" fracton behavior [43,45]. This global symmetry remains present in the dual gauge theory, enforcing onedimensional behavior on the dipoles.…”

“…Indeed, since superfluids exhibit effective non-conservation of particle number (via spontaneously broken U (1) symmetry), a system featuring coexisting crystalline and superfluid order (i.e. a supersolid) will host fully mobile dislocations [43,45]. Fracton-elasticity duality therefore indicates the presence of two distinct fracton phases at zero temperature, corresponding to the solid and supersolid phases, which are distinguished by the mobility of their dipole excitations.…”

“…Furthermore, the duality can be extended to include both the crystalline and superfluid sectors, thereby combining fracton-elasticity and particle-vortex dualities into one master bosonic duality. The resulting gauge dual of a two-dimensional supersolid is written in terms of both a symmetric tensor gauge field A ij and a vector gauge field a i , with an action given by [45]:…”

“…This connection is made precise via a duality transformation, often referred to as "fracton-elasticity duality," which maps the elasticity theory of crystals onto a symmetric tensor gauge theory [9]. We discuss this duality in detail in Section V, along with its various generalizations [41][42][43][44][45][46][47]. For example, the duality can be extended to three-dimensional elasticity theory, giving rise to the concept of fractonic lines, i.e line-like excitations without the ability to move [41].…”

On duality between Cosserat elasticity and fractons

“…The relationship between fracton phases of matter and elasticity has been noticed by several authors [36][37][38][39][40][41][42]. While formal details are different among these works, the essential observation is quite simple.…”