Antiferromagnetic spin ladders with odd and even numbers of chains

Abstract

We construct frustrated antiferromagnetic spin ladders with m chains for which the exact ground state can be determined in a particular parameter regime. The excitation spectrum is shown rigorously to be gapless (with gap) for odd (even) m. In a general parameter regime, the four-chain and periodic ladders are studied using a mean-field theory based on the bond operator formalism for spin S=. The excitation spectrum and the spin gap are calculated in both the cases. The spin gap of the frustrated ladder system has a larger magnitude than in the case of nonfrustrated ladders. For the frustrated periodic ladder, the spin gap vanishes at a critical value of the interladder coupling strength which is larger than the critical value in the case of nonfrustrated periodic ladders.