EPR Steering In Low-dimensional Spin Systems

In the past two decades,the relationship between some quantum symmetry correlations and the quantum phase transitions phenomenon in low-dimensional multi-body systems has attracted much attention,and many valuable research results have been achieved.In recent years,quantum steering,as an asymmetric form of quantum correlation,has begun to attract widespread attention.The relationship between steering and other correlations,such as Bell 's non-locality and quantum entanglement,has been clear,but the asymmetric is a unique property only existing in quantum steering.Quantum steering research is undoubtedly a very valuable part in quantum correlation studies.Compared by symmetry quantum correlations,this paper uses quantum steering as a tool for analyzing the quantum phase transitions in low-dimensional spin systems.First of all,the paper uses quantum steering to analyze the quantum phase transition phenomena in several spin models.For the anisotropic XY model,steering robustness approaches zero around the critical point and vanishes in the ferromagnetic phase,despite the quantum entanglement exists.For the Heisenberg XXZ model,steering robustness reaches its maximum around the quantum phase transition point,which exhibits similar behavior as entanglement.As a further example,this paper also considers steering robustness in the Lipkin–Meshkov–Glick collective spin model.It is shown that steering robustness disappears at the critical point and remains at zero in the fully polarized symmetric phase,just like the behavior of entanglement and Bell nonlocality.Afterwards,the paper studies quantum steering and quantum finite-size effect in the anisotropic XY model using quantum renormalization group method.Finite-size effect and critical exponents are considered in the model.The results show that the first derivative of steering robustness between two blocks diverges near the quantum phase transition points for this model,and exhibits a finite-size scaling effect.Moreover,the paper explores the asymmetric character of quantum steering,by taking into account finite–size effects and measurement number,in the reduced block state in the anisotropic XY model.The results imply that EPR steering for the reduced block state is asymmetric,but one-way steering does not exist.