Fermi liquids in the absence of charge quantization

Landau-Fermi liquid theory is a powerful tool to describe certain phases of strongly-correlated fermionic matter. However, at a quantum critical point, the emergent collective fluctuations of the order parameter couple to the bare electrons, resulting in scale-invariant behavior characterized by quantum critical exponents and the subsequent breakdown of a Fermi liquid picture. In the notorious "strange metal" non-Fermi liquid phase of the cuprate superconductors, such quantum critical scaling predicts the breakdown of charge quantization and a modified form of Maxwell's equations. In this work, I will explore the fate of a Fermi liquid in close proximity to such a critical point by calculating the RPA and non-RPA contributions to the quasiparticle lifetime for generalized Coulomb and Amperean quasiparticle interactions when charge quantization is absent. The vector potential's anomalous dimension is found to have strong and highly non-trivial influence on the lifetime in both cases, however there exists regimes of stability where a traditional, Luttinger's theorem-preserving Fermi liquid remains sensible. This work therefore opens new avenues to explore nearly-critical quantum matter with a Landau quasiparticle machinery.