The Study Of Thermodynamic Properties And Entanglement In Quantum Spin Systems

In the study of thermodynamic properties for many-body systems, Landau mean field theory is an important method. In this thesis, the thermodynamic properties of some quantum spin systems are studied by such a mean-field method. The entanglements in mixed-spin XY systems are investigated in detail as well. The main results are given as the following:1. The phase transition and thermodynamic properties of quantum Baxter-Wu model are studied. We find that the ground state is four-fold degenerate, which consists with the classical analysis. The thermal variations of the magnetization on each sub-lattice are obtained, which shows that the system exhibits a first-order phase transition at a finite temperature.2. The thermal variations of order parameters and phase diagrams of two kinds of spin-1 quantum Ising systems with three-spin interactions on two-dimensional triangular lattices are studied, and the order parameters with stable, metastable and unstable branches are obtained. We find that in phase diagrams there are the tricritical points for both systems and reentrant phase transitions for the system with crystal field and biquadratic interactions.3. The pairwise entanglements in (1/2, 1) mixed-spin XY systems are investigated by using of the concept of negativity. In the two- and four-qubit systems, the entanglement in ferromagnetic system is the same as that in the antiferromagnetic one. We find that there is a critical temperature above which the thermal entanglement vanishes, and that in two-qubit case the critical temperature is independent on the magnetic field.4. The entanglements in two-qubit (1/2,S) mixed-spin XY systems are studied. In the isotropic systems, the critical temperature is nearly proportional to the coupling constant J and the spin S. And the formula of the threshold magnetic field B_th above which the ground-state entanglement disappears as a function of spin S is given by B_th = (S/2)^1/2J. We find a first-order quantum phase transition point, T = 0, B = B_th, above which the negativity drops discontinuous to zero. For the case of zero magnetic field and temperature, there is the same negativity for all the systems that spin S is integer. For the systems that spin S is half integer, we have the same result.