Adiabatic tracking of a state: a new route to nonequilibrium physics.

We present a novel numerical approach to track the response of a quantum system to an external perturbation that is progressively switched-on. The method is applied, within the framework of the density matrix renormalization group technique, to track current-carrying states of interacting fermions in one dimension and in presence of an Aharonov-Bohm magnetic flux. This protocol allows us to access highly excited states. We also discuss the connection with the entanglement entropy of these excited states.