Field-Driven Correlated Quantum Systems, Bridging the Gap Between the Transient and the Steady State

Correlated quantum systems away from equilibrium have rightfully generated a lot of interest. Computational methods play an important role in understanding these systems but they are constrained by difficulties inherent to correlated systems that are exacerbated away from equilibrium. This prevents a full characterization of the dynamics. Previously, a set of relaxation scenarios were identified when systems initially in equilibrium are suddenly driven by a DC electric field. In particular, for certain parameters both the Hubbard and the Falicov-Kimball models evolve monotonically towards infinite temperature steady states that can be fully characterized by formulating solutions directly in the steady state. In the process these systems evolve through successive quasi-thermal states obeying the fluctuation dissipation theorem. We demonstrate an extrapolation scheme that can be leveraged to extend the characterization of the system from equilibrium to steady state at minimal computational cost. Namely, we extrapolate the monotonic temperature of the system and use the fluctuation dissipation theorem to construct the self-energy beyond the transient. All momentum dependent quantities can then be obtained within the DMFT formalism.