# Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models. (arXiv:1801.06178v1 [cond-mat.str-el])

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.