The Studies On Quantum Phase Transition Based On Quantum Fisher Information Matrix In Low-Dimensional Spin System

Quantum parameter estimation is the theoretical basis of quantum metrology,and quantum Cramér-Rao theorem is the most widely studied mathematical tool in quantum parameter estimation.In the quantum Cramér-Rao theorem,the quantum Fisher information matrix(QFIM)is the key quantity to characterize the accuracy limit of multi-parameters estimation.In recent years,people have done a lot of researches on quantum Fisher information matrix from different angles.However,there are still a lack of researches on the application of quantum Fisher information matrix in low dimensional spin system,so it is of great significance to study the application of quantum Fisher information matrix in low dimensional spin system.The research work of this paper mainly includes the following two aspects:First,from the perspective of the quantum Fisher information matrix,we study the quantum phase transition of the Ising-XXZ diamond model.Through the calculation and analysis of the quantum Fisher information matrix in the Ising XXZ diamond model,we reveal that the quantum Fisher information matrix can clearly characterize the quantum phase transition in the Ising XXZ diamond model.Furthermore,we find that the behavior of the quantum Fisher information matrix is not only related to the estimator variance,but also depends on the driving parameters at different quantum phase transition points;in multi-parameter estimation,multi-parameter simultaneous evaluation strategies are not always better than independent evaluation strategies has advantages and better precision.Secondly,we use the quantum Fisher information matrix to study the extended anisotropic XY spin chain model with nontrivial topological characteristics.The results show that the quantum Fisher information matrix can provide a useful tool for us to detect the topological critical points in the model.The behavior of quantum Fisher information matrix is not only related to the variance of estimators,but also depends on the driving parameters on quantum phase change dots with different topologies.At the same time,the choice of estimator also plays an important role in the behavior of quantum Fisher information matrix.