Learning emergent models from ab initio many-body calculations

The crucial step for understanding emergent low-energy physics is determining whether a particular model is emergent from ultraviolet physics. The state-of-the-art model derivation procedures, e.g., the constrained density functional theory and constrained random phase approximation, start from identifying a reduced Hilbert space using intuition and a given formulation of the effective models. While other methods, including the numerical renormalization group, do not require a priori information of the effective model but involve a choice of a logarithmic discretization scale on the spectrum and truncation of the Hilbert space by keeping the lowest-lying states. It would be preferable if the emergent degree of freedom could be learned without a priori knowledge using highly accurate many-body calculations since wave functions can be variationally improved.

In this study, we applied real-space variational quantum Monte Carlo to compute the many-body eigenstate wave functions for hydrogen chains. We then used unsupervised machine learning to cluster the ab initio many-body eigenstates based on various descriptors. The emergent spin degree of freedom described by the antiferromagnetic Heisenberg model was explicitly identified using the clustering model at large bond lengths. We highlight that the clustering of the ab initio eigenstates is not based on a pre-selected energy cutoff but learned using descriptors including total energy, spin-spin correlations, and double occupancies.