EXTENDED PROOF OF LONG-RANGE ORDER IN THE 2-DIMENSIONAL QUANTUM SPIN-1/2 XXZ-MODEL AT T = 0

We prove the existence of long-range order (LRO) in the ground state of the 2D quantum spin-1/2 XXZ-model for all anisotropies 0 less-than-or-equal-to DELTA less-than-or-equal-to 0.22 and DELTA greater-than-or-equal-to 1.47. We achieve this extension of previous proofs by developing an improved variant of the Dyson-Lieb-Simon proof of LRO in quantum spin systems and by deriving improved upper and lower bounds for the ground state energy of the XXZ-model.