Emergence of irrationality: Magnetization plateaus in modulated Hubbard chains

Hubbard chains with periodically modulated coupling constants in a magnetic field exhibit gaps at zero temperature in their magnetic and charge excitations in a variety of situations. In addition to fully gapped situations (plateau in the magnetization curve and charge gap), we have shown [Phys. Lett. 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 continuously on the filling n. Here we detail 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 temperatures (thus leading to a magnetization plateau) even in the presence of one massless mode. Next we study correlation functions and show that one component of the superconducting order parameter develops quasi-long-range order on a doping-dependent magnetization plateau. We then use perturbation theory 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 correlation functions by Lanczos diagonalization of finite clusters, confirming the presence of doping-dependent plateaus and their special properties.