The usefulness of restrictions for variational ground state lower bounds of a simple quantum spin lattice

We utilize reduced density matrices and restrictions upon them to obtain variational lower bounds to the ground state energy of the transverse Ising model. A systematic use of restrictions on a cluster representation (like 3 or 4 sites) of the system in 1, 2, and infinite dimensions, shows that a small class of conditions is sufficient to yield good results for little effort. The technique is analytically straightforward, and is clearly a promising direction to go for ground state energy bounds of quantum lattices with short range interactions.