Quantum Entanglement And Quantum Phase Transition In Solid-state Spin Systems

In this thesis, the quantum entanglement properties of one-dimensional solid-state quantum spin systems are investigated. By using the method of density matrix renormalization group, the ground state entanglement in different systems is studied. The ground-state entanglement and fidelity are applied to detect the quantum critical behavior—quantum phase transition.In the thesis, based on the different measurement of entanglement, the quantum entanglement properties of one-dimensional solid-state spin-1/2 systems are investigated by means of density matrix renormalization group. These systems include the antiferromagnetic Heisenberg spin chain with domain walls, the Ising model with alternating field, and the antiferromagnetic Heisenberg spin chain with boundary impurities. The ground state entanglement in the spin-1/2 isotropic antiferromagnetic Heisenberg chain is studied when the domain walls are generated by a boundary magnetic field. It is found that the pairwise entanglement of odd-bond two qubits decreases and even-bond two qubits increases when the magnetic field increases. The pairwise entanglement of odd-bond can equal to that of even-bond for a suitable value of the magnetic field. When the magnetic field increases further, the entanglement of even-bond can be larger than that of odd-bond. The entanglement entropy increases and then almost saturates as the number of spin sites increases. The entanglement entropy of odd-bond decreases to a minimum value and then increases as the magnetic field increases. For an opened Ising chain with an alternating magnetic field, the bipartite entanglement entropy decreases when the strength of the alternating field increases. The method of density matrix renormalization-group is applied to obtain logarithmic behavior of the entropy. It is found that the logarithmic behavior does not vary with the variation of the field. When the boundary impurities are imposed on the entanglement entropy in an anti-ferromagnetic Heisenberg opened spin-1/2 chain, the bipartite entanglement entropy increases when the length of the subsystem increases. It will approach to a constant due to the finite size of the system. With the same impurity interaction, qutrit-impurities of spin-1 can increase the entanglement entropy.By using the properties of quantum many-body theory and quantum-information theory, the ground state entanglement is applied to detect the critical behavior—quantum phase transition. The effects of anisotropy on the fidelity and the entanglement entropy are investigated. The relations between the fidelity, the entanglement entropy and the quantum phase transition are analyzed. The fidelity and the entanglement entropy in an antiferromagnetic-ferromagnetic alternating Heisenberg chain are investigated by using the method of density-matrix renormalization-group. It is found that the quantum phase transition point can be well characterized by both the fidelity and the ground-state entanglement entropy of the system. Furthermore, the quantum phase transition in an easy-axis antiferromagnetic Heisenberg spin-1 chain is numerically studied. It is found that the quantum phase transition from a spin liquid to spin solid can be well characterized by the fidelity susceptibility. The phase transition can be hardly detected by the entanglement entropy due to the monogamy property of the system while it can be detected by the first derivative of the entropy successfully.