SPIN GAPS IN COUPLED T-J LADDERS

Spin gaps in coupled t-J ladders are investigated by exact diagonalization of small clusters up to 4 X 8 sites. At half-filling, the numerical results for the triplet excitation spectrum are in very good agreement with a second-order perturbation expansion in terms of small interladder and intraladder exchange couplings between rungs (J/J'<0.25). The band of local triplet excitations moving coherently along the ladder (with momenta close to pi) is split by the interladder coupling. For intermediate couplings, finite-size scaling is used to estimate the spin gap. In the isotropic infinite four-chain system (two coupled ladders) we find a spin gap of 0.245J, roughly half of the single-ladder spin gap. When the system is hole doped, bonding and antibonding bound pairs of holes can propagate coherently along the chains and the spin gap remains finite.