Strongly Correlated Metal built from Sachdev-Ye-Kitaev Models

Prominent systems like high Tc cuprates and heavy fermions display intriguing features going beyond the quasiparticle description. The Sachdev-Ye-Kitaev(SYK) model provides a powerful framework to study such physics. It describes a 0+1D quantum cluster with random all-to-all \emph{four}-fermion interactions among N Fermion modes which becomes exactly solvable as N→∞, exhibiting a zero-dimensional non-Fermi liquid with emergent conformal symmetry and complete absence of quasi-particles. Here we study a lattice of complex-fermion SYK dots with random inter-site \emph{quadratic} hopping. Combining the imaginary time path integral with \emph{real} time path integral formulation, we obtain a heavy Fermi liquid to incoherent metal crossover in full detail, including thermodynamics, low temperature Landau quasiparticle interactions, and both electrical and thermal conductivity at all scales. We find linear in temperature resistivity in the incoherent regime, and a Lorentz ratio L≡κρT varies between two universal values as a function of temperature. Our work exemplifies an analytically controlled study of a strongly correlated metal.