The matrix product approach to quantum spin ladders

We present a manifestly rotational invariant formulation of the matrix prod uct method valid for spin chains and ladders. We apply it to two-legged spi n ladders with spins 1/2, 1 and 3/2 and different magnetic structures label led by the exchange coupling constants, which can be ferromagnetic or antif erromagnetic along the legs and the rungs of the ladder. We compute ground- state energy densities, correlation lengths and string order parameters. We present numerical evidence of the duality properties of the three differen t nonferromagnetic spin 1/2 ladders. We show that the long-range topologica l order characteristic of isolated spin 1 chains is broken by the interchai n coupling. The string order correlation function decays exponentially with a finite correlation length that we compute. A physical picture of the spi n 1 ladder is given in terms of a collection of resonating spin 1 chains. F inally, for ladders with spin equal to or greater than 3/2 we define a clas s of AKLT states whose matrix product coefficients are given by 9-j symbols .