Two- and three dimensional quantum-spin-1/2 XXZ magnets in zero magnetic field: global phase diagrams, thermodynamics and entanglement

Global phase diagrams and critical properties of the field-free quantum-spin-1/2 XXZ model in two- and three-dimensions are obtained using a numerical renormalization group theory method. Quantum phase transitions at zero-temperature are also identified. The nearest-neighbour spin-spin correlations and entanglement measures, as well as internal energy and specific heat are calculated globally at all temperatures for the whole range of exchange interaction anisotropy, from XY limit to Ising limits, for both antiferromagnetic and ferromagnetic cases. It is argued that there exists long-range (quasi-long-range) order at low-temperatures, and that the low-lying excitations are gapped (gapless) in the Ising-like easy-axis (XY-like easy-plane) regime.