Study of the critical behavior of a three-dimensional Heisenberg XXZ model via entanglement

Abstract

We investigate the characteristics of the Heisenberg anisotropic spin-12 XXZ model, in three dimensions, using the quantum coherence and the trace distance. By employing the iterative renormalization group scheme, we explore the thermodynamic limits of the system within the few iterations regime, leading to quantum phase transitions. Both quantifiers, the coherence, and the trace distance, hints at a transition between the spin fluid and the Néel phase of the model by attaining different saturated values. Additionally, a non-analyticity in the first derivative also accounts for the occurrence of a quantum phase transition at the critical point. Furthermore, we compute the critical exponents, from the scaling behavior of the quantifiers, which provide valuable insights into the system’s critical behavior. The correlation length is also described by the critical exponents. To strengthen the results obtained from the coherence and trace distance, concurrence is also examined. Overall, our findings contribute to a better understanding of the quantum properties and phase transitions in bulk crystals.