title: The phase diagram and hidden order for generalized spin ladders.
abstract: We investigate the phase diagram of antiferromagnetic spin ladders with additional exchange interactions on diagonal bonds by variational and numerical methods. These generalized spin ladders interpolate smoothly between the [Formula: see text] chain with competing nn and nnn interactions, the [Formula: see text] chain with alternating exchange and the antiferromagnetic (AF) S = 1 chain. The Majumdar - Ghosh ground states are formulated as matrix product states and are shown to exhibit the same type of hidden order as the AF S = 1 chain. Generalized matrix product states are used for a variational calculation of the ground state energy and the spin and string correlation functions. Numerical (Lanczos) calculations of the energies of the ground state and of the low-lying excited states are performed, and compare reasonably with the variational approach. Our results support the hypothesis that the dimer and Majumdar - Ghosh points are in the same phase as the AF S = 1 chain.
authors.affiliation: Institut für Theoretische Physik, Universität Hannover, 30167 Hannover, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Brehmer
authors.forename: H J
authors.initials: HJ
authors.lastname: Mikeska
authors.forename: U
authors.initials: U
authors.lastname: Neugebauer