Fractionalized Vortices Drive Kosterlitz-Thouless Transitions in Dipole-Conserving Systems

Abstract: Finite-temperature dipole-conserving superfluids in two dimensions pose a direct challenge to the usual Kosterlitz-Thouless (KT) paradigm: the primary phase field lacks quasi-long-range order, and the conventional vortex has only finite self-energy. We show that KT criticality nevertheless survives through a fractionalization of the vortex sector. In the dipole-conserving XY model, a minimal classical lattice realization of a fractonic superfluid, the conventional vortex is a finite-energy composite of two unconventional vortices in compact dipole fields. These fractionalized constituents have logarithmically divergent self-energies and are the defects that unbind at the transition; correspondingly, the ordinary helicity modulus remains nonsingular. Using Metropolis Monte Carlo supplemented by parallel tempering, generalized helicity moduli, and direct vortex-density measurements, we establish a phase diagram controlled by the deconfinement of these two vortex species. In the isotropic model, they deconfine simultaneously, producing a single KT transition. Coupling anisotropy splits the transition into two, separated by a phase with partial dipole quasi-long-range order, whereas removing the mixed-derivative coupling recombines the transitions even for anisotropic stiffnesses. Our theoretical and numerical results identify a fractionalized-defect mechanism for finite-temperature criticality in higher-moment-conserving matter and point to a hierarchy of KT transitions in multipole-conserving systems.