Multipartite Correlations And Thermal Tensor Networks In Low-dimensional Quantum Systems

Low-dimensional quantum spin systems have many rich physical phenomena and play a critical role in the field of condensed matter physics.In recent years,multipartite nonlocality,a concept from the field of quantum information,has been widely used to characterize quantum multipartite correlations.Previous papers mainly considered zero temperature.According to the third law of thermodynamics,materials in real environments are inevitably subject to thermal fluctuations,so it is of importance for the study of quantum systems at finite temperatures.The main work of this paper is as follows:First,in this paper,a complete set of numerical algorithms to calculate thermal-state multipartite nonlocality of finite-length quantum chains is completed.Currently,there is no mature,general open-source tool at finite temperatures.we programmed the code for thermal-state tensor networks for finite-length quantum chains using ITensor.In addition,the numerical calculation of multipartite nonlocality is very complicated,which to some extent hinders our in-depth analysis of the relevant results.Thereby,we have simplified the objective function in the numerical computation of multipartite nonlocality into a standard one-dimensional tensor network,which not only improves the computational efficiency but also provides a good foundation for the subsequent study of global nonlocality in the thermodynamic limit.Second,with the help of the thermal tensor network algorithm,we investigated the multipartite nonlocality in typical one-dimensional quantum models such as the Kitaev model,the XX model,and the XXZ model at finite temperatures.We found that in the Kitaev model,the nonlocality measure can indicate the topological quantum phase transition of the model;in the XX model,the nonlocality measure can indicate the magnetic phase transition of the model;in the XXZ model,the nonlocality measure can indicate the infinite-order quantum phase transition of the model.Furthermore,we quantitatively investigated the scaling behavior of multipartite nonlocality at finite temperatures.The result observed in this work complements the missing physical picture in the mid-temperature region since the behavior at low-and high-temperature limits had been researched by previous work.Third,based on the study of the simple one-dimensional quantum chain described above,we investigated the multipartite nonlocality of the quasi-one-dimensional ladder model and the trimerized model at finite temperatures,and analyzed the quantum phase transitions and the associated phase diagram in these models.The magnetic-field-induced oscillation behavior appears in the nonlocality curves of both models.Moreover,we analyzed the effect of temperature and sub-chain length on the magnetic-field-induced oscillation in the models.We discuss the effects of temperature and sub-chain length on the behavior of the oscillation separately.In particular,we researched the relationship between the number of peaks in the magnetic-field-induced oscillation and the length of the sub-chain,which has some theoretical significance for a deeper understanding of magnetic-field-induced oscillation.