Quantum Entanglement And Quantum Phase Transitions In Non-Hermitian XY Spin Systems

As we all know,the quantum entanglement is a property of quantum systems and has played an important role in various fields such as quantum mechanics,condensed matter physics and quantum information.In this thesis,the quantum entanglement and quantum phase transition are studied in the non-Hermitian XY model by using different methods.The main contents of this dissertation are summarized as follows:1.We study a non-Hermitian spin-1/2 XY system with two sites in the presence of an alternating,imaginary and transverse magnetic field.The eigenvalues and eigenstates of the Hamiltonian are exactly solved.In addition,the energy spectrum of the system is discussed and an exceptional point is obtained which distinguishes the parity-time reversal(PT)symmetry and symmetry broken phases.Then we study the ground-state phase diagram and find that there are two possible ground states.We further discuss the ground-state concurrence and find that it decreases with the real magnetic field h0 and increases with the anisotropy parameter γ when the ground state is only related to γ and h0,and it is always the maximum when the ground state only depends on the imaginary magnetic field η0,but the case is different for the case of the biorthogonal basis.When ground states are degenerate,the entanglement of the pure state which consists of two ground states is greater than that of the mixed state.In addition,the concurrence is calculated in the PT-symmetric broken region,and the imaginary magnetic field weakens the concurrence,which is the opposite of the case of the biorthogonal basis.Especially,the first derivative of concurrence shows the non-analytic behavior at the exceptional point,and the same is true in the case of the biorthogonal basis,which indicates that the concurrence can characterize the phase transition in this non-Hermitian system.We also study the thermal entanglement and find that η0 weakens it when the system is isotropic and enhances it when the system becomes the Ising model.Furthermore,when temperature approaches zero,there are overlapping parts between the thermal and non-degenerate ground-state entanglements and it is indicated that the thermal entanglement is realized by non-degenerate ground states.2.The quantum entanglement of the D-dimensional non-Hermitian XY spin system is studied by using the mean-field theory.By comparing the magnetization and the concurrence in the system of one-dimensional,it is found that their changing trends are opposite under certain conditions,that is,the concurrence decreases directly to zero with temperature,and the magnetization moment first decreases and then increases with temperature.In addition,the system exists the first-order quantum phase transitions for some anisotropic parameters in the PT-symmetry region,and the entanglement changes suddenly at the quantum phase transition point.The study also finds that the case of γ=1 is contrary to the situation of γ=0,at the moment,the concurrence increases with the increase of the imaginary magnetic field.It is indicated that the entanglement of the non-Hermitian system is larger than that of the Hermitian system in this case.Furthermore,the variations of the concurrence and the magnetization with each parameter are also studied in the two and three-dimensional cases.It is found that the concurrence and the magnetization decrease with the increase of temperature when γ=1.When the real magnetic field is small and γ=0.5,the magnetization first increases and then decreases with the increase of temperature.3.The Hamiltonian of a non-Hermitian XY spin system is solved exactly by using Jordan-Wigner and Bogoliubov transformations.We obtain the conditions of the full real energy spectrum and discuss the ground-state energy as well as magnetization of the system and find that the anisotropy parameter enhances the energy and weakens the magnetization,while the magnetic field is the opposite.We also study the variations of the entanglement with the parameters of system by using the concept of concurrence in the symmetry region.It is found that the concurrence decreases with the increase of the magnetic fields.Moreover,the larger the number of sites is,the smaller the concurrence,due to the monogamy of entanglement.When the number of sites approaches infinity,the entanglement tends to a stable value.In addition,the concurrence increases with the increase of the anisotropy parameter,which indicates that the non-Hermitian term enhances the entanglement at this time.At the exceptional point,the concurrence shows the non-analytic behavior,which indicates that the concurrence can characterize the phase transition in this non-Hermitian system.