By using the numerical renormalization group(NRG)method,we construct a large dataset with about one million spectral functions of the Anderson quantum impurity model.The dataset contains the density of states(DOS)of t...By using the numerical renormalization group(NRG)method,we construct a large dataset with about one million spectral functions of the Anderson quantum impurity model.The dataset contains the density of states(DOS)of the host material,the strength of Coulomb interaction between on-site electrons(U),and the hybridization between the host material and the impurity site(Γ).The continued DOS and spectral functions are stored with Chebyshev coefficients and wavelet functions,respectively.From this dataset,we build seven different machine learning networks to predict the spectral function from the input data,DOS,U,andΓ.Three different evaluation indexes,mean absolute error(MAE),relative error(RE)and root mean square error(RMSE),are used to analyze the prediction abilities of different network models.Detailed analysis shows that,for the two kinds of widely used recurrent neural networks(RNNs),gate recurrent unit(GRU)has better performance than the long short term memory(LSTM)network.A combination of bidirectional GRU(BiGRU)and GRU has the best performance among GRU,BiGRU,LSTM,and BiLSTM.The MAE peak of BiGRU+GRU reaches 0.00037.We have also tested a one-dimensional convolutional neural network(1DCNN)with 20 hidden layers and a residual neural network(ResNet),we find that the 1DCNN has almost the same performance of the BiGRU+GRU network for the original dataset,while the robustness testing seems to be a little weak than BiGRU+GRU when we test all these models on two other independent datasets.The ResNet has the worst performance among all the seven network models.The datasets presented in this paper,including the large data set of the spectral function of Anderson quantum impurity model,are openly available at https://doi.org/10.57760/sciencedb.j00113.00192.展开更多
In this work, we study the quantum steering in two-qubit Heisenberg models with Dzyaloshinskii–Moriya(DM)interaction and an external magnetic field. We find that the steerable weight(SW) and the critical temperature ...In this work, we study the quantum steering in two-qubit Heisenberg models with Dzyaloshinskii–Moriya(DM)interaction and an external magnetic field. We find that the steerable weight(SW) and the critical temperature where SW → 0 can be enhanced by the DM interactions. In the special case where the magnetic field is vanishing and the two spins are ferromagnetically coupled, the DM interaction can tune the zero-temperature SW from zero to a finite value. In addition to the SW, some other measurements used to identify the quantum entanglement and quantum correlations are investigated, i.e., the concurrence, the quantum discord, and the robustness of coherence. In the strong magnetic field limit,our results show that the SW is dramatically different from the other measurements.展开更多
We study three important measurements used to identify the quantum correlations between two quantum dots （QDs） mediated by a pair of Majorana fermions （MFs） in a superconducting quantum wire. We find that, in addi...We study three important measurements used to identify the quantum correlations between two quantum dots （QDs） mediated by a pair of Majorana fermions （MFs） in a superconducting quantum wire. We find that, in addition to the quantum discord, the robustness of coherence （ROC） can also be considered as a quantity to measure the quantum correlation for the special case where the quantum entanglement is vanishing. For comparison, we study the quantum correlation between two QDs mediated by other fermions, i.e., regular fermions and superconducting fermions. We find that, when the quantum entanglement is not vanishing, i.e., the concurrence is finite, the detailed difference between the concurrence and ROC can be considered as an important implication for the existence of MFs.展开更多
We study two-dimensional massive Dirac equation in circular well potential. The energies of bound states are obtained. We demonstrate the Klein paradox of this relativistic wave equation:For large enough potential dep...We study two-dimensional massive Dirac equation in circular well potential. The energies of bound states are obtained. We demonstrate the Klein paradox of this relativistic wave equation:For large enough potential depth, the bound states disappear from the spectra. Applications to graphene systems are discussed.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.12174101)the Fundamental Research Funds for the Central Universities(Grant No.2022MS051)。
文摘By using the numerical renormalization group(NRG)method,we construct a large dataset with about one million spectral functions of the Anderson quantum impurity model.The dataset contains the density of states(DOS)of the host material,the strength of Coulomb interaction between on-site electrons(U),and the hybridization between the host material and the impurity site(Γ).The continued DOS and spectral functions are stored with Chebyshev coefficients and wavelet functions,respectively.From this dataset,we build seven different machine learning networks to predict the spectral function from the input data,DOS,U,andΓ.Three different evaluation indexes,mean absolute error(MAE),relative error(RE)and root mean square error(RMSE),are used to analyze the prediction abilities of different network models.Detailed analysis shows that,for the two kinds of widely used recurrent neural networks(RNNs),gate recurrent unit(GRU)has better performance than the long short term memory(LSTM)network.A combination of bidirectional GRU(BiGRU)and GRU has the best performance among GRU,BiGRU,LSTM,and BiLSTM.The MAE peak of BiGRU+GRU reaches 0.00037.We have also tested a one-dimensional convolutional neural network(1DCNN)with 20 hidden layers and a residual neural network(ResNet),we find that the 1DCNN has almost the same performance of the BiGRU+GRU network for the original dataset,while the robustness testing seems to be a little weak than BiGRU+GRU when we test all these models on two other independent datasets.The ResNet has the worst performance among all the seven network models.The datasets presented in this paper,including the large data set of the spectral function of Anderson quantum impurity model,are openly available at https://doi.org/10.57760/sciencedb.j00113.00192.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11504106,11805065,11247308,and 11447167)the Fundamental Research Funds for the Central Universities,China(Grant Nos.2018MS049 and 2018MS056)
文摘In this work, we study the quantum steering in two-qubit Heisenberg models with Dzyaloshinskii–Moriya(DM)interaction and an external magnetic field. We find that the steerable weight(SW) and the critical temperature where SW → 0 can be enhanced by the DM interactions. In the special case where the magnetic field is vanishing and the two spins are ferromagnetically coupled, the DM interaction can tune the zero-temperature SW from zero to a finite value. In addition to the SW, some other measurements used to identify the quantum entanglement and quantum correlations are investigated, i.e., the concurrence, the quantum discord, and the robustness of coherence. In the strong magnetic field limit,our results show that the SW is dramatically different from the other measurements.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11504106,11247308,and 11447167)the Fundamental Research Funds for the Central Universities of China(Grant Nos.2018MS049 and 2018MS057)
文摘We study three important measurements used to identify the quantum correlations between two quantum dots （QDs） mediated by a pair of Majorana fermions （MFs） in a superconducting quantum wire. We find that, in addition to the quantum discord, the robustness of coherence （ROC） can also be considered as a quantity to measure the quantum correlation for the special case where the quantum entanglement is vanishing. For comparison, we study the quantum correlation between two QDs mediated by other fermions, i.e., regular fermions and superconducting fermions. We find that, when the quantum entanglement is not vanishing, i.e., the concurrence is finite, the detailed difference between the concurrence and ROC can be considered as an important implication for the existence of MFs.
基金Supported by the Fundamental Research Funds for the Central Universitiesthe National Natural Science Foundation of China under Grant No.10904111
文摘We study two-dimensional massive Dirac equation in circular well potential. The energies of bound states are obtained. We demonstrate the Klein paradox of this relativistic wave equation:For large enough potential depth, the bound states disappear from the spectra. Applications to graphene systems are discussed.
