Factorized ground state in dimerized spin chains

The possibility of observing factorized ground states in dimerized spin systems is studied. A set of sufficient conditions is derived which allows one to establish whether or not it is possible to have factorization both in nearest-neighbour and long-range Hamiltonians. These conditions can be derived by forcing factorization for each of the pairwise terms of the total Hamiltonian. Due to the peculiar structure of a dimerized chain, an antiferromagnetic factorized ground state of the kind |nearr), |nearr), |nwarr), |nwarr) (forbidden in regular chains) is possible.