Emergence of irrationality: Magnetization plateaus in modulated Hubbard chains - art. no. 094406

Hubbard chains with periodically modulated coupling constants in a magnetic field exhibit gaps at zero temperature in their magnetic and charge excita tions in a variety of situations. In addition to fully gapped situations (p lateau in the magnetization curve and charge gap), we have shown [Phys. Let t. A 268, 418 (2000)] that plateaus also appear in the presence of massless modes, leading to a plateau with a magnetization m whose value depends con tinuously on the filling n. Here we derail and extend the arguments leading to such doping-dependent magnetization plateaus. First we analyze the low- lying excitations using Abelian bosonization. We compute the susceptibility and show that due to the constraint of fixed n, it vanishes at, low temper atures (thus leading to a magnetization plateau) even in the presence of on e massless mode. Next we study correlation functions and show that one comp onent of the superconducting order parameter develops quasi-long-range orde r on a duping-dependent magnetization plateau. We then use perturbation the ory in the on-site repulsion U to compute the width of these plateaus up to first order in U. Finally, we compute ground state phase diagrams and corr elation functions by Lanczos diagonalization of finite dusters, confirming the presence of doping-dependent plateaus and their special properties.