Extended proof of long-range order in the two-dimensional quantum spin-1/2 XXZ-model at T=0

Hans-Aloys Wischmann; Erwin Müller-Hartmann

doi:doi:10.1051/jp1:1991109

Numéro		J. Phys. I France Volume 1, Numéro 5, May 1991


Page(s)		647 - 657
DOI		https://doi.org/10.1051/jp1:1991109

DOI: 10.1051/jp1:1991109
J. Phys. I France 1 (1991) 647-657

Extended proof of long-range order in the two-dimensional quantum spin-1/2 XXZ-model at T=0

Hans-Aloys Wischmann and Erwin Müller-Hartmann

Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, D-W 5000 Köln 41, Germany

(Received 25 January 1991, accepted 1 February 1991)

Abstract
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 $0\leqslant\Delta\leqslant 0.22$ and $\Delta\geqslant 1.47$ . 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.