Coexistence of insulating phases in confined fermionic chains with a Wannier-Stark potential

We study fermions on a finite chain, interacting repulsively when residing on the same and on nearest-neighbor sites, and subjected to a Wannier-Stark linearly varying potential. Using the density matrix renormalization-group numerical technique to solve this generalized extended Hubbard model, the ground state exhibits a staircase of (quasi) plateaus in the average local site density along the chain, decreasing from being doubly filled to empty as the potential increases. These ``plateaus'' represent locked-in commensurate phases of charge density waves together with band and Mott insulators. These phases are separated by incompressible regions with incommensurate fillings. These results differ from the many-body localization proposed for this model earlier. It is suggested that experimental variations of the slope of the potential and the range of the repulsive interactions will produce such a coexistence of phases which have been individually expected theoretically and observed experimentally for uniform systems.