Quantum Phase Transitions In The DM Interaction XY Model And Pairing Symmetries In Unconventional Superconductors

In this paper,our research content mainly has two directions.The first research direction is that quantum coherence and quantum manipulation are used to characterize quantum phase transitions in XY models with DM interactions.The second research direction is to learn the pairing symmetry of disordered superconductors by using the local density of states with spin polarization.We study the quantum steering and quantum coherence in the generalized XY model with Dzyaloshinskii-Moriya interaction in the first research direction.We find that both Steerable Weight(SW)and Robustness of Coherence(ROC)can be applied to describe the quantum phase transition in this model.Steerable weight and robustness of coherence,which are applied to qualify quantum steering and quantum coherence,respectively.As the strength of Dzyaloshinskii-Moriya interaction increases,the phase transition characterized from the derivative of robustness of coherence becomes less significant.This is dramatically different from steerable weight.As the strength of Dzyaloshinskii-Moriya interaction increases,the identification of quantum phase transition from steerable weight becomes more accurate.In addition,numerical investigations show that a sufficiently large number of random measurements in each assemblage is important in the calculation of steerable weight and the identification of quantum phase transition.We construct an artificial neural network to study the pairing symmetries in disordered superconductors in the second research direction.For Hamiltonians on square lattice with s-wave,d-wave,and nematic pairing potentials,we use the spin-polarized local density of states near a magnetic impurity in the clean system to train the neural network.We find that,when the depth of the artificial neural network is sufficient large,it will have the power to predict the pairing symmetries in disordered superconductors.In a large parameter regime of the potential disorder,the artificial neural network predicts the correct pairing symmetries with relatively high confidences.