The Frenkel line and the Widom line: analogies between classical and electronic fluids

The Mott critical point is in the Ising universality class, the same universality class as the gas-liquid critical point of water. The supercritical state of water exhibits distinct liquid-like and gas-like regions [1, 2]. In this work, we construct analogies between these two different systems, classical liquids and electronic liquids. It is known that above the critical point in classical liquids like CO2, H2O and Ar, there is a Widom line where maxima and various crossovers of thermodynamic quantities are observed. On the triangular lattice Hubbard model, where magnetic orders are frustrated, it has already been shown that in the supercritical region above the Mott transition, there is an analogous Widom line [3] associated with crossovers. We investigate whether the Frenkel line proposed to dynamically distinguish the supercritical liquid from the supercritical gas [2] also exists in the electronic liquid. We base our results on calculations of the optical conductivity using the dynamical cluster approximation.

[1] C. Cockrell et K. Trachenko, Science Advances 8, eabq5183 (2022).

[2] V. V. Brazhkin et al., Physical Review E 85, 031203 (2012).

[3] P.-O. Downey et al., Physical Review B 107, 125159 (2023).