Charge fluctuations, hydrodynamics and transport in the square-lattice Hubbard model

Abstract

Recent experimental results suggest that a particular hydrodynamic theory describes charge fluctuations at long wavelengths in the square-lattice Hubbard model. Due to the continuity equation, the correlation functions for the charge and the current are directly connected: the parameters of the effective hydrodynamic model thus determine the optical conductivity. Here we investigate the validity of the proposed hydrodynamic theory in the full range of parameters of the Hubbard model. In the non-interacting case, there is no effective hydrodynamics, and the charge fluctuations present a rich variety of non-universal behaviors. At weak coupling, the optical conductivity is consistent with the hydrodynamic theory: at low frequency one observes a Lorentzian-shaped Drude peak, but the high-frequency asymptotics is necessarily different; the high-temperature limit for the product of the two hydrodynamic model parameters is also in agreement with numerical data. At strong coupling, we find that a generalization of the proposed hydrodynamic law is consistent with our quantum Monte Carlo, as well as the finite-temperature Lanczos results from literature. Most importantly, the temperature dependence of the hydrodynamic parameters as well as the dc resistivity are found to be very similar in the weak and the strong-coupling regimes.