Linear in temperature resistivity and the many-body Kubo formula

The description of dynamics of strongly correlated quantum matter is a challenge, particularly in situations where a quasiparticle description is absent. In such situations, however, the many-body Kubo formula from linear response theory still remains valid. We address the puzzle of linear in temperature (T-linear) resistivity seen in non-Fermi liquid phases that occur in several condensed matter systems. We derive a simple criterion for the occurence of T-linear resistivity based on an analysis of the contributions to the many-body Kubo formula, determined by an invariant “f-function" involving current matrix elements and energy eigenvalues that describes the DC conductivity of the system in the microcanonical ensemble. Using full diagonalization, we test this criterion for the f-function in several different models - the spinful Fermi Hubbard model and the spinless nearest neighbor Hubbard model, and in lattices of Sachdev-Ye-Kitaev models with single particle hopping. We also discuss a shift-invert algorithm to compute the f-function on lattice sizes where Krylov techniques can be applied.