Quantum phase transition and entanglement in XXZ Heisenberg spin chain

Using the quantum renormalization group approach, we have investigated the entanglement and critical behavior of an anisotropic XXZ Heisenberg spin chain. The resolution of the quantum renormalization equations yields stable and unstable fixed points, corresponding respectively to the phases and critical point of the system. It is shown that a quantum phase transition exists at a critical anisotropy parameter $\Delta _{c} = 1$ , separating the Néel phase from the spin-fluid phase. Then, the concurrence between two blocks of sites and the quantum coherence have been calculated and presented for various renormalization group iterations. In the thermodynamic limit, i.e., for higher renormalization steps, the concurrence and coherence exhibit two different saturated values in the two regions separated by Δc. The first derivative of concurrence diverges at the critical point as the size of the chain increases, showing nonanalytic behavior. Moreover, the scaling behavior has been examined near the critical point with some universal exponential scaling laws.