Low-energy properties of regularly depleted spin ladders

Abstract

We investigate a model for the regularly depleted two-leg spin-ladder systems. By using the 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 in 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 nonlinear sigma model, and confirm that the massless-spin excitation indeed occurs.