Learning crystal field parameters using convolutional neural networks

Abstract

We present a deep machine learning algorithm to extract crystal field (CF) Stevens parameters from thermodynamic data of rare-earth magnetic materials. The algorithm employs a two-dimensional convolutional neural network (CNN) that is trained on magnetization, magnetic susceptibility and specific heat data that is calculated theoretically within the single-ion approximation and further processed using a standard wavelet transformation. We apply the method to crystal fields of cubic, hexagonal and tetragonal symmetry and for both integer and half-integer total angular momentum values JJ of the ground state multiplet. We evaluate its performance on both theoretically generated synthetic and previously published experimental data on CeAgSb_22, PrAgSb_22 and PrMg_22Cu_99, and find that it can reliably and accurately extract the CF parameters for all site symmetries and values of JJ considered. This demonstrates that CNNs provide an unbiased approach to extracting CF parameters that avoids tedious multi-parameter fitting procedures.

Predicting quantum potentials by deep neural network and metropolis sampling

“…These problems are critical in many numerical and experimental setups, such as designing the exchange-correlation potentials in the ab-initio simulations of material [17,18], the analytic continuation of the imaginary Green's function into the real frequency domain [19], and designing quantum simulators [20]. One topic that currently attracts wide interests is to estimate the Hamiltonian given the states or their properties [21][22][23][24][25][26]. Considering the quantum lattice models, for example, it has been proposed to predict the coupling constants from the measurements of the target states [27][28][29] or the local reduced density matrices [30].…”