Frustration-nonfrustration Structure And Quantum Correlations In A Triangular Ising Model

In the past decade,quantum correlation as a unique quantum resource,has not only been widely used in the field of quantum information,but also attracted great attention in the field of condensed matter physics,such as quantum phase transition,quantum many body physics,quantum frustration structure and so on.The study of frustration structure is an important topic in condensed matter physics.Quantum frustration can produce a large number of degenerate states,which makes it of practical application value in microelectronic physics,especially in data storage.In addition,the entangled ground state caused by frustration is closely related to exotic quantum materials such as quantum spin liquids and spin glasses.The simplest frustration structure is the transverse Ising spin system in a triangular configuration,in which the ground state of the system and its quantum correlations will be significantly affected when the coupling strength among the spins changes.Most of the physical systems with the triangle Ising structure in nature are asymmetrically coupled.In recent years,asymmetrically coupled triangular frustration structures have been realized experimentally in artificial structures such as nuclear magnetic resonance systems,superconducting systems and cold atomic systems,and their physical ground state can be used as an important resource for quantum information processing.In order to further characterize the ground state properties of the frustration structure,it is desirable to study the effect of asymmetrical coupling on the multipartite quantum correlations.On the other hand,we can also use the properties of the quantum correlations in the ground state to indicate the property of the phase diagram for the triangular Ising structure.In this thesis,we mainly study the influence of asymmetrical coupling on the quantum correlations of the ground states of the frustration and nonfrustration in the triangle transverse field Ising model,and analyze the thermal robustness of the three-qubit quantum correlations in the thermal states of different quantum phases at finite temperature.In particular,we derive the analytical relation between the structure scale of frustration and nonfrustration and the three-qubit quantum correlation in the presence of the asymmetrical coupling between the spins.On the other hand,by studying the thermal robustness of the quantum correlations in different quantum phases at finite temperature,we find that the three-qubit quantum correlation of the frustration structure is more robust than that of the nonfrustration one.For some specific coupling parameters,the thermal robustness of the multipartite quantum correlations in the frustration structure is really obvious,which provides a strong theoretical tool for realizing the thermal-robust multipartite quantum correlation state by modulating the asymmetrical coupling in experiment and then carrying out the effective quantum information processing.This thesis is divided into three chapters.In Chapter I,we mainly introduce the characterization on multipartite quantum correlations based on entanglement monogamy and their application in quantum phase diagrams for many-body systems.In Chapter II,we give the analytical expression for the ground state and its three-qubit negativity in a triangular transverse Ising model with symmetrical and asymmetrical coupling,and then study the influence of the asymmetrical coupling on the three-qubit negativity of the two structures.In Chapter III,we study the thermal robustness of three-qubit quantum correlation in the triangular Ising model.We find that the multipartite quantum correlation in frustration structures are always more robust than that in the nonfrustration structures,and especially for some specific asymmetrical coupling parameters,the thermal robustness of the system is very strong.