Critical phenomena and quantum discord of quantum antiferromagnetic Heisenberg model on diamond-type hierarchical lattices

The anisotropic spin-1/2 antiferromagnetic Heisenberg systems are studied on three typical diamond-type hierarchical lattices (systems A, B and C) with fractal dimensions df=1.63, 2 and 2.58, respectively. For system A, using the real-space renormalization group approach, we calculate the phase diagram, the critical exponent and quantum discord, and find that there exists a reentrant behavior in the phase diagram. We also find that the quantum discord reaches its maximum at T=0 and the thermal quantum discord decreases with the increase of L, and it is almost zero at L>30. No matter how large the size of system is, quantum discord will change to 0 when anisotropic parameter Delta=1. For systems B and C, using the equivalent transformation and the real-space renormalization group method, we obtain phase diagrams and find that: the Neel temperature tends to zero in the isotropic Heisenberg limit on df=2 system; there exists a phase transition in the isotropic Heisenberg model on system C. By studying quantum discord, we find that there is a certain degree of twist of the relation curve between quantum discord and T when Delta=0. Moreover, as an example, we discuss the quantum effect in system A, which can be responsible for the existence of the reentrant behavior in the phase diagram.