Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting

Abstract

Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.

Entanglement in the quantum Hall fluid of dipoles

“…dislocations) has been noted by previously, e.g. in [32][33][34], where it signals a "quantum melting" transition.…”

Space-Dependent Symmetries and Fractons

“…So far we have discussed the case of a global symmetry. However, certain spin liquids [2,22,23], and elastic fields [5,[33][34][35] contain a gauged version of the symmetry discussed here. In fact, a generalization of electrodynamics [2] to account for systems with the class of conservation laws discussed here has been constructed.…”

“…Nonetheless, if we were to allow the gauge fields to propagate in curved space, the gauge principle seems to enter in conflict with diffeomorphism transformations [5,36]. In [25] Slagle, Prem, and Pretko argued that in two space dimensions the fracton gauge invariance will not be broken as long as the space is an Einstein manifold, and more recently [34,35] the fractonic gauge symmetry has been extended to volume preserving diffeomorphisms and connected to the lowest Landau level.…”

“…More recently various extensions of the original elastic dualities have been proposed. These include Cosserat elasticity with antisymmetric degrees of freedom [49][50][51][52], elasticity with smectic anisotropy [53], vortex lattices [34], elasticity of quasicrystals [54] and elasticity with underlying moiré lattices [55]. In addition, folding and tearing can have an interpretation as being fractonic [56].…”

Vortices as fractons

“…One prominent yet down-to-earth example of excitations with restricted mobility is crystalline defects in quantum crystals and liquid crystals [49][50][51][52][53][54][55][56][57] . There, dislocations satisfy the glide constraint that forces them to move along their Burgers vector, while disclinations are immobile.…”