Low-Energy Properties of Regularly Depleted Spin Ladders

We investigate a model for the regularly depleted two-leg spin ladder systems. By using Lieb-Schultz-Mattis theorem, it is rigorously shown that this model realizes massless excitations or, alternatively, a degenerate ground state, although the original spin ladder system has a spin gap and a unique ground state. The ground state of the depleted model is either a spin singlet or partially ferromagnetic reflecting topological properties of the depleted sites. In order to show that the low-energy excitations are indeed massless, we proceed our analysis in two different ways by resorting to effective field theories. We first investigate an effective weak-coupling model in terms of renormalization group methods. Although the tendency to massless spin excitations is seen in the strong coupling regime, it turns out that the model is still massive for any finite coupling, implying that a conventional weak-coupling approach is not efficient to describe massless modes in our model. To overcome this difficulty, we further study low-energy properties of the depleted spin model by mapping on the non-linear sigma model, and confirm that the massless spin excitation indeed occur.