Dynamics of Quantum Correlation in Two-Qubit Heisenberg XYZ Hamiltonian With Nonuniform Magnetic Field

In this paper we investigate the quantum correlation(geometric quantum discord and quantum entanglement) in two-qubit Heisenberg XYZ Hamiltonian with Dzyaloshinskii-Moriya interaction and Kaplan-Shekhtman-Entin-Wohlman-Aharony interaction under the effect of nonuniform external magnetic field. Here, we calculate the effect of nonuniform magnetic field, exchange interaction Jx,Jy,Jz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${J}_{x},{J}_{y},{J}_{z}$$\end{document}, Dzyaloshinskii -Moriya interaction D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D$$\end{document} and Kaplan-Shekhtman-Entin-Wohlman-Aharony interaction Gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma$$\end{document} on the quantum correlation`dynamics in case of the antiferromagnetism. The results obtained reveal that the nonuniform part of the external magnetic field plays the important role in the preservation of quantum correlation. Also, it is shown that the geometric quantum discord is more robust than the quantum entanglement and the effect of the different parameters on the quantum correlation` dynamic depend noticeably on choice of initial state.Graphical AbstractIn Fig. 13, we indicate the time evolution of GQD and QE for various b=1,1.5,2,4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b=1,1.5,2,4$$\end{document} with =0.99,gamma=1,Jx=2,Jy=1.5,,Jz=1,D=0.5,Gamma=0.2,B=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$=0.99,\gamma =1,{J}_{x}=2,{J}_{y}=1.5,,{J}_{z}=1,D=0.5,\Gamma =0.2,B=1$$\end{document}.