Multipartite Quantum Nonlocality And Topological Quantum Phase Transitionsin Low-Dimensional Quantum Systems

In recent years,quantum correlation which is growing rapidly has attracted widespread attention in the field of condensed matter physics.Multipartite quantum nonlocality is a physical quantity for characterizing thecorrelation structure of multipartite quantum correlations in quantum states.In thispaper,we firstly investigate several typical quantum models,such asJ₁-J₂chain with next-nearest-neighbor interactions、XXZ model on a zigzag lattice and i.e..It has been reported that multipartitequantum nonlocality is singular at the quantum phase transitions（QPTs）points,thus can beused to detect and characterize topological QPTs.Moreover,we will use the newly developed nonlocality-transfer-matrixtheory to characterize the scaling behavior of multipartite quantum in one-dimensional quantum chains.Up to now,we have obtainedmany valuable results as follow:（1）For J₁-J₂ chain with next-nearest-neighbor interactions,it can be seen that multipartite quantum nonlocality provide quite sharp signals for the topological QPTs between the even-Haldane phase and the odd-Haldane phase.Nevertheless,in these two phases,the spread of the multipartite quantum nonlocality among the lattice is different.When Bell-type experiments are carried out on odd-bond subchains,the high hierarchy of multipartite quantum nonlocality can be observed in the odd-Haldane phase but not in the even-Haldane phase.When even-bond chains are considered,the result is reversed.Moreover,we find that the footprints of the multipartite quantum nonlocality survive at low temperatures,thus,based upon the scaling behavior of the finite-temperature nonlocality measure,we propose a quantity K to characterize the finite-temperature nonlocality in the large-n limit.We find that in high-temperature regions,K is reduced linearly as the temperature rises.Therefore,we have a linear scaling formula of multipartite quantum nonlocality at finite temperatures.（2）For XXZ model on a zigzag lattice,the model is derived from polar molecules under an electric field,and its ground states can undergo topological QPTs between a singlet dimer（SD）phase and an even-parity dimer（ED）phase.We use multipartite quantum nonlocality to characterize these topological QPTs.We find that the nonlocality measure,which is defined on the reduced density matrices for odd-bond subchains,can act as an order parameter for the topological QPTs.In the SD phaseand in the vicinity of the phase boundary,is relatively large.In most regions of the ED phase,nevertheless,is nearly zero.Therefore,it is an effective physical quantity for multipartite quantum nonlocality to characterize topological QPTs.After all,we investigate the scaling behavior of multipartite quantum nonlocality,and obtain the same linear scaling formula inJ₁-J₂chain with next-nearest-neighbor interactions.（3）We will use nonlocality-transfer-matrix theory to investigate QPTs inJ₁-J₂chain with next-nearest-neighbor interactions and transverse-field Ising model.The theory reveals the hidden translation invariance in the multipartite quantum nonlocality operators in one-dimensional（1D）quantum chains and will show that in the large-n limit,multipartite quantum nonlocality₉)is just determined by the largest-magnitude eigenvalue₈（6）of the transfer matrix in the model,i.e.,₉)～₈（6）⁹).It offers a unified description for the scaling behaviors of multipartite quantum nonlocality in general quantum chain models.Furthermore,based on this discovery,a new algorithm for calculating multipartite quantum nonlocality is proposed.In quantum critical regions,the algorithms converge much faster than the traditional approach.In summary,we will characterize various quantum critical phenomena from an intuitive perspective of“global correlation structure”.Moreover,the eigenvalue spectrum of the nonlocality-transfer matrix would provide us a concise and profound mathematical structure behind the related critical behaviors.We believe this project will increase our understanding about multipartite quantum correlations and quantum criticality in one-dimensional quantum systems.