The usefulness of quantum concepts in soft matter: quasiparticles, flat bands, and the melting of hydrodynamic crystals

The concept of quasiparticles---long-lived low-energy particle-like excitations---has become a keystone of condensed quantum matter, where it explains a variety of emergent many-body phenomena, such as superfluidity and superconductivity. Here, we will use quasiparticles to examine the collective behavior of a classical system of hydrodynamically interacting particles in two dimensions. In the disordered phase of this matter, measurements show a sub-population of long-lived particle pairs. Modeling and simulation of the ordered crystalline phase identify the pairs as effective quasiparticles, emerging at the Dirac cones of the spectrum and inducing the melting of the crystal. When the intrinsic threefold symmetry of the hydrodynamic interaction matches that of the crystal, the cones connect to a multicritical, monkey-saddle van Hove singularity, forming a nearly-flat band of slow low-frequency excitations whose divergent density drives a sharper melting transition. Altogether, these findings demonstrate the usefulness of concepts from quantum matter theory in understanding many-body physics in classical dissipative settings.