Disordered ground states in a quantum frustrated spin chain with side chains

We study a frustrated mixed spin chain with side chains, where the spin species and the exchange interactions are spatially varied. A nonlinear sigma model method is formulated for this model, and a phase diagram with two disordered spin-gap phases is obtained for typical cases. Among them, we examine the case with a main chain, which consists of an alternating array of spin-1 and spin- = 1/2 sites, and side chains, each of which consists of a single spin-1/2 site, in great detail. Based on numerical, perturbational, and variational approaches, we propose a singlet cluster solid picture for each phase, where the ground state is expressed as a tensor product of local singlet states.