  We construct examples of translationally invariant solvable models of
strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with
identical local interactions. These models display crossovers as a function of
temperature into regimes with local quantum criticality and marginal-Fermi
liquid behavior. In the marginal Fermi liquid regime, the dc resistivity
increases linearly with temperature over a broad range of temperatures. By
generalizing the form of interactions, we also construct examples of non-Fermi
liquids with critical Fermi-surfaces. The self energy has a singular frequency
dependence, but lacks momentum dependence, reminiscent of a dynamical mean
field theory-like behavior but in dimensions $d<\infty$. In the low temperature
and strong-coupling limit, a heavy Fermi liquid is formed. The critical
Fermi-surface in the non-Fermi liquid regime gives rise to quantum oscillations
in the magnetization as a function of an external magnetic field in the absence
of quasiparticle excitations. We discuss the implications of these results for
local quantum criticality and for fundamental bounds on relaxation rates.
Drawing on the lessons from these models, we formulate conjectures on coarse
grained descriptions of a class of intermediate scale non-fermi liquid behavior
in generic correlated metals.
