The problem of strongly interacting gapless fermions above one dimension is one of the wildest open frontiers in quantum condensed matter where our understanding remains insular and embedded in vast oceans of mystery. In this talk, I will describe certain islands of this knowledge dealing with the collective behaviour of strongly interacting Fermi surfaces of electrons and of spinons and describe new experimental strategies to probe them.
For electrons, I will discuss the emergence of a bizarre collective shear wave that is absent in classical fluids and that resembles the transverse sound of crystalline solids in spite of the system remaining in a fluid state that lacks any proper form of static crystallinity or shear modulus. There is no conclusive detection of this shear sound wave to this date, however, I will show that this mode gives rise to sharp dips in the conductance of interacting clean metallic channels when driven at frequencies that resonantly excite its standing waves.
For spinons, I will discuss their spectrum of low lying excitations by employing a generalisation of higher dimensional bosonization of Fermi surfaces coupled to a U(1) gauge field. I will demonstrate that their transverse electric conductivity at low frequencies has a universal form dictated only by fundamental constants of nature and the geometry of their fermi surface. This universal transverse conductivity of spinons is identical to that of ordinary metals, in spite of their longitudinal conductivity resembling that of an electric insulator. I will show how this universal transverse conductivity can be measured from the magnetic noise outside the sample that can be probed with NV centers. Such observation would provide a smoking gun for the presence of the elusive spinon fermi surface state in correlated materials.