A variational method based on weighted graph states

In a recent article Anders et al 2006 Phys. Rev. Lett. 97 107206, we have presented a class of states which is suitable as a variational set to find ground states in spin systems of arbitrary spatial dimension and with long-range entanglement. Here, we continue the exposition of our technique, extend from spin 1/2 to higher spins and use the boson Hubbard model as a non-trivial example to demonstrate our scheme.