Local criticality and marginal Fermi liquid behavior in a translationally invariant solvable model I : Thermodynamics and single particle properties

An ubiquitous feature across many strongly-correlated materials is the appearance of a metallic phase without well defined quasiparticle excitations and non-Fermi liquid properties. The non-Fermi liquid properties often persist over a broad range of temperatures above a small crossover scale, below which conventional Fermi liquid behavior is recovered. In this work, we construct examples of translationally invariant models of strongly-correlated metals with on-site, multi-orbital interactions of the Sachdev-Ye-Kitaev form. When the number of orbitals is taken to be large, we observe interesting crossovers as a function of increasing temperature from a renormalized Fermi liquid with a sharp Fermi surface to a non-Fermi liquid regime with local quantum criticality and no sign of a Fermi-surface. By extending the model to have multiple bands with different bandwidths, we also construct examples of marginal and non-Fermi liquid metals with a critical Fermi surface and singular self-energy. We discuss the thermodynamic properties and compute the single-particle spectral functions in the different regimes.