Skew Information And Its Application In Quantum Many-body Systems

Wigner and Yanase study the theory of mechanics from the perspective of information theory,they first put forward the Wigner-Yanase skew information theory.In recent years,Wigner–Yanase skew information theory has been extensively studied.It is closely related to the quantum correlation quantities from the quantum information theory.Therefore,this thesis is devoted to the quantum correlation quantities with related to the Wigner–Yanase skew information as a powerful tool to characterize the quantum phase transition and quantum criticality of various one-dimensional quantum systems.We explore quantum uncertainty,based on Wigner–Yanase skew information,in various one-dimensional single-electron wave functions.For the power-law function and eigenfunctions in the Aubry–André model,the electronic localization properties are well-defined.For them,we find that quantum uncertainty is relatively small and large for delocalized and localized states,respectively.And around the transition points,the first-order derivative of the quantum uncertainty exhibits singular behavior.All these characters can be used as signatures of the transition from a delocalized phase to a localized one.With this criterion,we also study the quantum uncertainty in one-dimensional disorder system with long-range correlated potential.The results show that the first-order derivative of spectrum-averaged quantum uncertainty is minimal at a certain correlation exponent ? m for a finite system,and has perfect finite-size scaling behaviors aroundm?.By extrapolatingm?,the threshold value 1.56 0.02c? ? ? is obtained for the infinite system.Thus we give another perspective and propose aconsistent interpretation for the discrepancies about localization property in the long-range correlated potential model.These results suggest that the quantum uncertainty can provide us with a new physical intuition to the localization transition in these models.On the other hand,we explore quantum coherence,inherited from Wigner-Yanase skew information,to analyze quantum criticality in the anisotropic XY chain model at finite temperature.Based on the exact solutions of the Hamiltonian,the quantum coherence contained in a nearest-neighbor spin pairs reduced density matrix ? is obtained.The first-order derivative of the quantum coherence is non-analytic around the critical point at sufficient low temperature.The finite-temperature scaling behavior and the universality are verified numerically.In particular,the quantum coherence can also detect the factorization transition in such a model at sufficient low temperature.We also show that quantum coherence contained in distant spin pairs can characterize quantum criticality and factorization phenomena at finite temperature.Our results imply that quantum coherence can serve as an efficient indicator of quantum criticality in such a model and shed considerable light on the relationships between quantum phase transitions and quantum information theory at finite temperature.