Field-free quantum-spin-1/2 XXZ model in three-dimensions: phases, phase transitions, and phase diagrams by renormalization group theory

Abstract

The field-free quantum-spin-1/2 XXZ model is studied in three-dimensions using renormalization grouptheory. We obtain global phase diagrams and critical properties. We identify zero-temperature quantum phase transitionsat isotropic points, as well as long-range order below critical temperatures at all anisotropies. We show that the excitationspectrum is gapless in XY-like, and gapped in Ising-like anisotropy regimes. Besides, internal energy density, specificheat, nearest-neighbor entanglement measures and spin-spin correlations are obtained globally at all temperatures. Ournumerical results cover the global range of anisotropy parameter, for both ferromagnetic and antiferromagnetic cases.