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 obta in variational lower bounds to the ground state energy of the transver se Ising model. A systematic use of restrictions on a cluster represen tation (like 3 or 4 sires) of the system in 1, 2, and infinite dimensi ons, shows that a small class of conditions is sufficient to yield goo d results for little effort. The technique is analytically straightfor ward, and is clearly a promising direction to go for ground state ener gy bounds of quantum lattices with short range interactions.