An analogy between classical and electronic fluids in the triangular Hubbard model

In classical fluids, the Frenkel line marks a dynamical crossover between liquid-like and gas-like states, separating regimes of oscillatory and diffusive particle motion in the supercritical regime. We demonstrate an analogous phenomenon in correlated electronic fluids living on the half-filled triangular-lattice Hubbard mode, that we solved using the dynamical cluster approximation [1]. Above the Mott critical end-point, we find a sharp crossover from a correlated Fermi liquid to a pseudogap regime. Using the sign change of the optical conductivity in real-time, σ₁(t) < 0, as a marker of back-scattering onset, we define an electronic Frenkel line that extends from the Mott critical point to high temperatures. This line complements, yet remains distinct from, other crossover markers such as the Widom line [2] and the first-order metal–metal (“Sordi”) transition upon doping [3]. Our work bridges concepts from classical and electronic fluids, offering an experimentally accessible criterion for dynamical crossovers in correlated materials.