Generalized Hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model

Abstract

We have studied nonequilibrium dynamics of the one-dimensional Hubbard model using the generalized hydrodynamic theory. We mainly investigated the spatio-temporal profile of charge density, energy density and their currents using the partitioning protocol; the initial state consists of two semi-infinite different thermal equilibrium states joined at the origin. In this protocol, there appears around the origin a transient region where currents flow. We examined how density and current profiles depend on initial conditions and have found a clogged region where charge current is zero but nonvanishing energy current flows. This region appears when one of the initial states has half-filled electron density. We have proved analytically the existence of the clogged region in the infinite temperature case of the half-filled initial state. The existence is confirmed also for finite temperatures by numerical calculations. A similar analytical proof is also given for a clogged region of spin current when magnetic field is applied to one and only one of the two initial states. A universal proportionality of charge and spin currents is also proved for a special region, for general initial conditions of electron density and magnetic field. Except for the clogged region, charge and energy densities are in good proportion to each other, and their ratio depends on the initial conditions. This proportionality in nonequilibrium dynamics is reminiscent of Wiedemann-Franz law in thermal equilibrium. The long-time stationary values of charge and energy currents were also studied with varying initial conditions. We have compared the results with the values of non-interacting systems and discussed the effects of electron correlations. We have found that the temperature dependence of the ratio of these stationary currents is strongly suppressed by electron correlations and even reversed.