Long-range effective interactions in a lattice in the semiclassical approximation

We consider the semiclassical model of an extended tight-binding Hamiltonian comprising nearest- and next-to-nearest-neighbor interactions for a charged particle hopping in a lattice in the presence of a static arbitrary field and a rapidly oscillating uniform field. The application of Kapitza's method yields a time-independent effective Hamiltonian with long-range hopping elements that depend on the external static and oscillating fields. Our calculations show that the semiclassical approximation is quite reliable as it yields, for a homogeneous oscillating field, the same effective hopping elements as those derived within the quantum approach. Besides, by controlling the oscillating field, we can engineer the interactions so as to suppress the otherwise dominant interactions (nearest neighbors) and leave as observable effects those due to the otherwise remanent interactions (distant neighbors).