Study On Quantum Correlations In Some One - Dimensional Spin Chains

Quantum phase transition (QPT) is one of the most important subjects in the field of condensed matter physics. Traditionally, QPT is described in the framework symmetry broken and order parameter within the Ginzburg-Landau paradigm. Recently, with the rapid development of the quantum information theory (QIT), the study of QPTs from the perspective the QIT becomes an active research topic. The dissertation focus on the relation between several quantum information concepts and the QPTs in some typical one dimensional (1D) quantum spin models. The concepts are quantum discord, quantum entanglement, quantum coherence and quantum uncertainty, etc. The last part of this dissertation briefly discusses the dynamics of quantum uncertainty.First, the size effect of ground state quantum discord between the nearest neighbors in the 1D transverse-field anisotropic XY model is studied, it is found that, for the Ising transition, the critical behaviors of the derivatives of the quantum discord close to the critical point (CP) are dependent on the anisotropy parameter, however, for the anisotropy transition, the size effect of the derivatives of the quantum discord close to the CP system have the logarithmic divergence with the system size for any external fields, which are different from the behaviours of quantum entanglement in the model.Secondly, the ground state quantum discord in the 1d transverse-field anisotropic XY chains with XZY - YZX type three-spin interactions has been studied. Compared with the 1D transverse-field anisotropy XY model, there is also a gapless chiral phase, besides the usual gapped ferromagnetic (FM) and paramagnetic (PM) phases in the model with three-spin interactions. It is found that the first-order derivative of the quantum discord at the Ising type transition between the gaped FM and PM phases has a logarithmic divergence scaling with the system size. However, the first-order derivative of the quantum discord at the CPs of the QPTs between the gaped and the gapless phases does not increase with the system size. For the transverse field isotropic XY chain, there are two gapless chiral phases in the model, and the first-order derivatives of the quantum discord at CPs of the QPTs between the two gapless phases have a similar behavior with those between the gaped and gapless phases.Next, the quantum coherence based on Wigner-Yanase skew information and its re-lations with QPTs in 1D transverse-field XY model are studied. For the Ising transition, the first-order derivatives of quantum coherence at the CP all have logarithmic divergence with the chain sizes, for the anisotropy transition, the single-spin quantum coherence and the two-spin local σz quantum coherence are extremal at the CP, and the first-order derivatives of the two-spin local σx and σy quantum coherence have logarithmic diver-gence with the chain sizes, interestingly, with completely opposite slopes and intercepts. However, for the model with three-spin interactions, no finite-size scaling behavior of the derivatives of quantum coherence is found at the CPs of the QPTs between the gapped FM or PM phase and the gapless chiral phase. A simplified version of coherence is also studied and the similar characteristic to its counterpart is found.Finally, the dynamics of the quantum uncertainty in the nearest neighbors of 1D XY spin chain in a step-like time-dependent transverse-field are calculated, the effect of temperature on the dynamic is also discussed. It is found from the time evolution that both the entanglement and the uncertainty are non-ergodic, and the non-ergodicity roots in the magnetization and spin correlation functions of the system.