Dissociation of a Hubbard--Holstein bipolaron driven away from equilibrium by a constant electric field

Using a variational numerical method we compute the time-evolution of the Holstein-Hubbard bipolaron from its ground state when at t=0 the constant electric field is switched on. The system is evolved taking into account full quantum effects until it reaches a quasi-stationary state. In the zero-field limit the current shows Bloch oscillations characteristic for the adiabatic regime where the electric field causes the bipolaron to evolve along the quasiparticle band. Bipolaron remains bound and the net current remains zero in this regime. At larger electric fields the system enters the dissipative regime with a finite steady-state current. Concomitantly, the bipolaron dissociates into two separate polarons. By examining different parameter regimes we show that the appearance of a finite steady-state current is inevitably followed by the dissociation of the bipolaron.