Many-body energy invariant for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi></mml:math> -linear resistivity

The description of the dynamics strongly correlated quantum matter is a challenge, particularly in physical situations where quasiparticle absent. In such situations, however, many-body Kubo formula from linear response theory, involving matrix elements current operator computed with wave functions, remains valid. Working directly Hilbert space and not making any reference to quasiparticles (or lack thereof), we address puzzle temperature ($T$-linear) resistivity seen non-Fermi-liquid phases that occur several condensed systems. We derive simple criterion for occurrence $T$-linear based on an analysis contributions formula, determined by energy invariant ``$f$ function'' eigenvalues describes dc conductivity system microcanonical ensemble. Using full diagonalization, test this $f$ function spinless nearest-neighbor Hubbard model Sachdev-Ye-Kitaev dots coupled weak single-particle hopping. also study spin two-dimensional Heisenberg arrive at similar conclusions. Our work suggests general principle, formulated terms concepts, core wide range systems, precisely translates into notion scale invariance far beyond what typically associated critical points.