Anisotropic Xy Chain With Dm Interaction Quantum Phase Transitions, Quantum Entanglement And Thermal Entanglement

The study of quantum phase transitions and critical phenomena is one of the most important problems in agglomerate physics. Thereinto, quantum Heisenberg model is the most, simple model and have been extensively researched. In recent years, because of the potential applications of DM interaction and the effects to the critical phenomena of quantum chain coursed by DM interaction, it has been studied extensively. So we will study the quantum phase transitions of quantum XY chain with DM interaciou. Recently, many researches had found that we can study quantum phase transitions by the method of quantum entanglement, so we will also study the quantum entanglement of this model.At first, Quantum phase transitions and entanglement of anisotropic XY chain with Dzyaloshinskii-Moriya (DM) interaction in a transverse field have been studied. The phase diagram is obtained by the studies of order parameters, ground-state energy and entanglement. Besides paramagnetic phase and ferromagnetic phase, a new chiral phase is found after the introduction of the DM interaction. In this new phase the von Neumann entropy SL is proportional to A log2 L with the coefficient A≈1/3 as same as that in the anisotropy transition line of XY chain without DM interaction. When 0< D< 0.5, the Ising transition is also happening at h= 1. In this critical line, SL is proportional to Alog2 L with A≈1/6 as same as that in the Ising transition line of XY chain without DM interaction. When D> 0.5, ferromagnetic phase will disappear.Then, the concurrence at limited temperature of this system were studied. We found that in the region ofγ≥2D, the.behavior of concurrence is independent of the value of D, there are also three critical temperature points when 0<γ<γc(γc=0.3875). While at the region ofγ<2D, whenγ-γc, there will appear there critical temperature points along with the increase of the value of D. We also studied the the von Neumann'entropy at limited temperature of this system, we give the behavior of von Neumann entropy with the change of temperature, external magnetic field and the length of sub-chain.