Research On The Multipartite Nonlocality Of Low-dimensional Spin System

Quantum correlation in quantum spin systems is one of the research hotspots in quantum information and condensed matter physics.Correlation information quantities such as entanglement entropy can capture dramatic changes in the degree of quantum correlation in a system,so such quantities are often used to characterize quantum phase transitions.However,for many-body quantum systems,in addition to the strong and weak changes of the correlation degree,the correlation structure can also have rich changes.Multipartite nonlocality is a many-body quantum correlation physical quantity that characterizes the correlation structure,which gives us a very intuitive understanding of how quantum systems are correlated.Therefore,studying multipartite nonlocality in quantum systems will deepen our understanding of quantum phase transitions and critical phenomena in low-dimensional quantum spin systems from a novel and interesting perspective.In this paper,we use the exact diagonalization method and the tensor network algorithm to systematically study the multipartite nonlocality of the one-dimensional Ising model and one-dimensional transverse field Ising model with longitudinal magnetic field(Mixed-order Ising).And the conclusions are as follows:(1)First,we study the behavior of multipartite nonlocality in one-dimensional Ising models of finite and infinite chain.For the finite chains,we use the exact diagonalization method to calculate the multipartite nonlocality of the small system in the ground state,that is,the ground-state multipartite nonlocality.The results show that the logarithm of the ground state multipartite nonlocality is linearly related to the particle number N.At the same time,we also use the exact diagonalization method and the thermal tensor network algorithm to explore the multipartite nonlocality behavior of N≤ 14 and N> 14 at finite temperature,namely thermal multipartite nonlocality.The results show that thermal multipartite nonlocality peaks near the phase transition point,so multipartite nonlocality at finite temperature can be used to characterize quantum phase transitions.The results also show that the logarithm of the thermal multipartite nonlocality and the number of particles N satisfy a linear relationship.For the infinite chain,we study their thermal multipartite nonlocality behavior with the help of the infinite thermal tensor network algorithm.The results show that the infinite chains exhibit similar behavior to the finite chains,that is,the thermal multipartite nonlocality versus magnetic field peaks,however,the peak position of the thermal multipartite nonlocality is compared with the finite chains.Move to a larger magnetic field,and its peak is lower than the finite chain.The logarithm of the thermal multipartite nonlocality of infinite chains also satisfies a linear relationship with the local chain length n.(2)Second,we study the multipartite nonlocality behavior of the onedimensional finite-size Mixed-order Ising model at the ground state and finite temperature.For ground state,ground-state multipartite nonlocality behaviors for N≤ 14 and N> 14 are investigated using the exact diagonalization method and ALPS,respectively.ALPS can overcome the limitation that the exact diagonalization algorithm can only solve small systems.The results show that the ground state multipartite nonlocality can find the footprint of the phase transition.When the interaction between the longitudinal magnetic field and the nearest neighbor is constant,the logarithm of the ground state multipartite nonlocality increases linearly with the number of particles.For the finite temperature,the thermal multipartite nonlocality exhibits different behavior from the ground state,and we give a general explanation for this difference.Again,the results show that the logarithm of multipartite nonlocality at finite temperature satisfies a linear relationship with the number N of particles.