Cyclic spin exchange in cuprate spin ladders

We investigate the influence of a cyclic spin exchange Jcyc on the one- and two-triplet excitations of an undoped two-leg $S=1/2$ ladder, using the density-matrix renormalization group (DMRG). The dispersion of the $S=0$ two-triplet bound state is dramatically reduced by Jcyc due to a repulsion between triplets on neighboring rungs. In (La,Ca)₁₄Cu₂₄O₄₁ a consistent description of both the spin gap and the S=0 bound state requires Jcyc/J_⊥≈0.20--0.27 and J/J_⊥≈1.25--1.35. With these coupling ratios the recently developed dynamical DMRG yields an excellent description of the entire $S=0$ excitation spectrum observed in the optical conductivity, including the continuum contribution.