Quantum phase transition and entanglement in XXZ Heisenberg spin chain

¹ Laboratory LPMC, Faculty of Sciences, Chouaib Doukkali University - El Jadida, Morocco
² LS2ME Laboratory, Polydisciplinary Faculty of Khouribga, Sultan Moulay Slimane University - Beni Mellal, Morocco
³ Higher School of Education and Training (ESEF), Chouaib Doukkali University - El Jadida, Morocco

Received: 4 January 2025
Accepted: 21 May 2025

Abstract

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 , 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 Δ_c. 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.