Driven single-band tight-binding dynamics, mesoscopic quantum circuits and realization of generalized parafermionic polynomial algebrasDeformed parafermionic algebra from single-band tight-binding dynamics

The quantum dynamics of a driven single-band tight-binding model with different boundary conditions is considered. The relation between the Hamiltonian describing the single-band tight-binding dynamics and the Hamiltonian of a discrete-charge mesoscopic quantum circuit is elucidated. It is shown that the former Hamiltonian, with Dirichlet boundary conditions, can be considered as a realization of the deformed parafermionic polynomial algebras.