We studied the dynamic correlations of non-integrable systems with quantum many-body scar(QMBS)states generated by a ladder operator.The ladder operator's spectral function has an exact δ-function peak induced by...We studied the dynamic correlations of non-integrable systems with quantum many-body scar(QMBS)states generated by a ladder operator.The ladder operator's spectral function has an exact δ-function peak induced by the QMBS states.As a concrete example,we show that in the one-dimensional(1D)spin-1 Affleck-Kennedy-Lieb-Tasaki model,the spectral function of two-magnon excitations exhibits a characteristic bowtie shape composed of aδ-function resonance peak at momentum k=π and a continuum spectrum elsewhere.The two-magnon excitations can be observed via resonant inelastic X-ray scattering spectroscopy on quasi-1D nickelates and other spin-1 antiferromagnetic materials.Therefore,the findings of this study pave the way for detecting(approximate)QMBS states in realistic materials.展开更多
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
基金supported by the National Natural Science Foundation of China(Grant No.12174387)the Chinese Academy of Sciences(Grant Nos.YSBR-057 and JZHKYPT-2021-08)the Innovative Program for Quantum Science and Technology(Grant No.2021ZD0302600)。
文摘We studied the dynamic correlations of non-integrable systems with quantum many-body scar(QMBS)states generated by a ladder operator.The ladder operator's spectral function has an exact δ-function peak induced by the QMBS states.As a concrete example,we show that in the one-dimensional(1D)spin-1 Affleck-Kennedy-Lieb-Tasaki model,the spectral function of two-magnon excitations exhibits a characteristic bowtie shape composed of aδ-function resonance peak at momentum k=π and a continuum spectrum elsewhere.The two-magnon excitations can be observed via resonant inelastic X-ray scattering spectroscopy on quasi-1D nickelates and other spin-1 antiferromagnetic materials.Therefore,the findings of this study pave the way for detecting(approximate)QMBS states in realistic materials.
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.
