Hydrodynamics of dipole-conserving fluids

Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and immobile excitations' dubbed fractons. Unfortunately, such systems have so far escaped a complete macroscopic formulation as viscous fluids. In this work, we construct a consistent hydrodynamic description for fluids invariant under translation, rotation, and dipole shift symmetry. We use symmetry principles to formulate a thermodynamic theory for dipole-conserving systems at equilibrium and apply irreversible thermodynamics in order to elucidate dissipative effects. Remarkably, we find that the inclusion of the energy conservation not only renders the longitudinal modes diffusive rather than subdiffusive but also diffusion is present even at the lowest order in the derivative expansion. This work paves the way towards an effective description of many-body systems with constrained dynamics such as ensembles of topological defects, fracton phases of matter, and certain models of glasses.

Figure 1

Trajectories of the longitudinal modes in the frequency complex plane as a function of the thermal conductivity at fixed momentum with arrows indicating the direction of increase in thermal conductivity. (a) Frequencies as a function of the thermal conductivity for $a_1/a_2=0.75{(a_1/a_2)}_c$. (b) Longitudinal modes in the critical regime ${(a_1/a_2)}_c$, the collision of the modes happens at $a_2=\sqrt{3}$. (c) Trajectories in Regime II for $a_1/a_2=1.25{(a_1/a_2)}_c$.