In this talk, I will address the following question: what properties of metals are universal in the sense that they hold not just in particular models or theories (e.g. Landau's Fermi liquid theory), but in any (clean) metal, even strongly coupled non-Fermi liquids? I will argue that progress can be made on this question by elevating compressibility - that is, the property that the emergent low-temperature behavior is compatible with a continuous range of electron densities - as the defining feature of a metal. I will argue that compressibility is sufficient to deduce various properties, such as the existence of a Fermi surface that obeys Luttinger's theorem. Furthermore I will apply hydrodynamics to the associated emergent conserved quantities to derive the equation of motion for the low-frequency, long-wavelength collective dynamics of a metal and show that it reduces to the same kinetic equation that in Fermi liquid theory governs the dynamics of the quasiparticles (leading me to coin the term "quasi-quasiparticles"). I will explain how non-hydrodynamic modes can nevertheless restore some non-Fermi-liquid-like behavior in the dynamics. The results of this talk illustrate the power of the concept of emergent symmetries as a tool to understand the physics of strongly coupled systems.
Host: Hae-Young Kee