Quantum Correlation In Heisenberg Model

Quantum correlation as a good abstract of quantum resources,it is widely used in the fields of quantum communication and quantum computing.Two of the most representative types of quantum correlations are quantum entanglement and quantum discord.They have been used to achieve quantum teleportation,quantum key distribution,quantum coding,and quantum computing.Quantum entanglement is not completely equivalent to non-classical associations.In the study of the Heisenberg model,it was found that when the quantum entanglement is zero,there is still a quantum mismatch,so people have a lot of interest in quantum mismatch,but in many cases It is difficult to calculate the quantum mismatch,and only some special states can obtain accurate analytical solutions of quantum mismatch.To overcome this problem,Dakic et al.Proposed a geometric quantum mismatch,which has analytical solutions for all systems.We studied the ground state entanglement,thermal entanglement,geometric quantum mismatch and quantum phase transition of anisotropic Heisenberg XYZ spin chain system under a non-uniform magnetic field,as well as changes with external magnetic field,temperature,and anisotropic parameters.This article mainly studies the following aspects:The first chapter introduces the theory of quantum information,and the model of quantum entangled states and Heisenberg spin chains after two revolutions;The second chapter introduces the origin of qubits,density matrices,quantum phase transitions,and measurement methods of quantum correlation between two-body systems,such as: negative eigenvalues of some devices,formation of entanglement,and geometric quantumdiscord;The third chapter uses the formation entanglement degree as the entanglement metric to study the Heisenberg XYZ model of double qubits in a non-uniform magnetic field.The properties of the ground state entanglement in different parameters are calculated.The critical magnetic field values are calculated by calculation.The relationshipbetween the magnetic field and the critical magnetic field and the quantum phase transition.The interaction between the spin components of two adjacent qubits and the anisotropy parameters are analyzed.The effect on the thermal entanglement of the Heisenberg model is illustrated by plotting the images The relationship between anisotropy,spin coupling parameters,and thermal entanglement.The results show that in a dual qubit system,for effective temperature,when the coupling parameter is equal to 0,as the anisotropy increases,the critical magnetic field decreases and the entanglement gradually disappears;but when the coupling parameter is greater than 0,the The anisotropy parameter takes a proper value.With the increase,the magnetic field range and temperature range where the degree of entanglement reaches the maximum become larger,and the entanglement can be effectively enhanced.The fourth chapter studies the thermal geometric quantum discord characteristics of the double qubit Heisenberg XYZ spin chain,and the effects of temperature and magnetic field anisotropy parameters on thermal entanglement and thermal geometric quantum discord in different magnetic field environments.The results show that the effects of different magnetic fields on quantum correlations are not the same at finite temperatures.No matter how the magnetic field changes,the thermal geometric quantum discord is more resistant to changes in the external environment than thermal entanglement;for higher temperatures The external magnetic field has a great influence on the behavior of geometric quantum discord,and when the thermal entanglement is equal to zero,the thermal geometric quantum discord still exists;in addition,the non-uniform magnetic field can expand the magnetic field range of the thermal entanglement and the thermal geometric quantum discord.In chapter 5,the thermon quantum discord in the three-bit Heisenberg XXZ model with DM interaction is studied.In the antiferromagnetic and paraferromagnetic chains,the DM interaction,the external magnetic field,and temperature affect the quantum discord influences.The results of the study show that: in both antiferromagnetic and paraferromagnetic chains,the quantum discord eventually stabilizes with the increase of the DM interaction.The higher the temperature before the value of the quantum discord stabilizes,The larger the applied magnetic field,thesmaller the value of the quantum discord.Therefore,we can regulate the generation and manipulation of quantum correlation through the interaction of external magnetic field,temperature and DM.