Machine learning of Kondo physics using variational autoencoders and symbolic regression

Abstract

We employ variational autoencoders to extract physical insight from a dataset of one-particle Anderson impurity model spectral functions. Autoencoders are trained to find a low-dimensional, latent space representation that faithfully characterizes each element of the training set, as measured by a reconstruction error. Variational autoencoders, a probabilistic generalization of standard autoencoders, further condition the learned latent space to promote highly interpretable features. In our study, we find that the learned latent variables strongly correlate with well known, but nontrivial, parameters that characterize emergent behaviors in the Anderson impurity model. In particular, one latent variable correlates with particle-hole asymmetry, while another is in near one-to-one correspondence with the Kondo temperature, a dynamically generated low-energy scale in the impurity model. Using symbolic regression, we model this variable as a function of the known bare physical input parameters and "rediscover" the non-perturbative formula for the Kondo temperature. The machine learning pipeline we develop suggests a general purpose approach which opens opportunities to discover new domain knowledge in other physical systems.

Update to match PRB publication + typo fixes + minor edits

References in corpus (5)

• The numerical renormalization group method for quantum impurity systems
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression
• Exploring order parameters and dynamic processes in disordered systems via variational autoencoders
• Predicting impurity spectral functions using machine learning

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• Autoencoder-based analytic continuation method for strongly correlated quantum systems
• Hamiltonian parameter inference from resonant inelastic x-ray scattering with active learning