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Fractonic superfluids are exotic states of matter with spontaneously brokenhigher-rank $U(1)$ symmetry. The latter is associated with conserved quantitiesthat include not only particle number (i.e. charge) but also higher moments,such as dipoles, quadrupoles, and angular moments. Due to the presence of suchconserved quantities, the mobility of particles is restricted either completelyor partially. In this work, we systematically study hydrodynamical propertiesof fractonic superfluids, especially focusing on the fractonic superfluids withconserved angular moments. The constituent bosons are called "lineons" with$d$-components in $d$-dimensional space. From Euler-Lagrange equation, wederive the continuity equation and Navier-Stokes-like equations, in which theangular moment conservation introduces extra terms. Furthermore, we discuss thecurrent configurations that are related to the defects. Like the conventionalsuperfluid, we study the critical values of velocity fields and densitycurrents, which gives rise to a Landau-like criterion. At the end of this work,several future directions are discussed.

Quantum Hydrodynamics of Fractonic Superfluids with Lineon Condensate: from Navier-Stokes-like Equations to Landau-like Criterion