Fractonic superfluids, topological vortices, and quantum fluctuations

We propose an exotic superfluidity---fractonic superfluid, which is a many-body system of non-relativistic bosonic fractons. As one of most salient features of fractons, the single-fracton motion is forbidden since both total charge and total dipole moments are conserved. We start with a \nth{2} quantized microscopic model and formulate the coherent-state path-integral representation. In the presence of the usual Mexican-hat potential, we calculate various properties and make comparison between fractonic superfluid and conventional superfluid. We deduce the highly nonlinear Euler-Lagrange equation as well as Noether currents. We also formulate time-dependent Gross-Pitaevskii-type equations that govern hydrodynamical behaviors. We study the classical ground state wavefunction, the associated off-diagonal long range order (ODLRO), and unconventional topological vortices. Gapless Goldstone modes and specific heat capacity at low temperatures are obtained. Then, the fate of Goldstone modes and ODLRO in the presence of quantum fluctuations is investigated. The calculation shows that ODLRO at zero temperature is ultimately unstable against quantum fluctuations unless the spatial dimension is larger than two. More general many-fracton systems with higher rank symmetry are also considered. Several future directions are discussed.