Non-linear response to electric field in extended Hubbard models

Abstract

The electric-field response of a one-dimensional ring of interacting fermions, where the interactions are described by the extended Hubbard model, is investigated. By using an accurate real-time propagation scheme based on the Chebyshev expansion of the evolution operator, we uncover various non-linear regimes for a range of interaction parameters that allows modeling of metallic and insulating (either charge density wave or spin density wave insulators) rings. The metallic regime appears at the phase boundary between the two insulating phases and provides the opportunity to describe either weakly or strongly correlated metals. We find that the {\it fidelity susceptibility} of the ground state as a function of magnetic flux piercing the ring provides a very good measure of the short-time response. Even completely different interacting regimes behave in a similar manner at short time-scales as long as the fidelity susceptibility is the same. Depending on the strength of the electric field we find various types of responses: persistent currents in the insulating regime, dissipative regime or damped Bloch-like oscillations with varying frequencies or even irregular in nature. Furthermore, we also consider the dimerization of the ring and describe the response of a correlated band insulator. In this case the distribution of the energy levels is more clustered and the Bloch-like oscillations become even more irregular.