2008/04/30 by R. Jafari, Mehdi Kargarian, M. Kargarian +3 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Critical phenomena #Critical point (mathematics) #Fixed point #Ising model #Mathematics #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum #Quantum critical point #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Renormalization #Renormalization group #Scaling #Spin (aerodynamics) #Spin model #Theoretical and Computational Physics #Thermodynamics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.78.214414
11page, 15 figures, Accepted in Physical Review B
arxiv created 2008/11/18 · openalex publication_date 2008/12/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We have studied the phase diagram and entanglement of the one-dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization-group (QRG) approach to get the stable fixed points, critical point, and the scaling of coupling constants. This model has two phases: antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite-size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of spin operators which are defined by a nonlocal transformation.