Learning minimal representations of fermionic ground states

Physical Review Research, vol. 8

Abstract

We introduce an unsupervised machine-learning framework that discovers optimally compressed representations of quantum many-body ground states. Using an autoencoder neural network architecture on reduced density matrix data from L -site Fermi-Hubbard models, we identify minimal latent spaces with a sharp reconstruction quality threshold at L − 1 latent dimensions, matching the system's intrinsic degrees of freedom. We demonstrate the use of the trained decoder as a differentiable variational ansatz to minimize energy directly within the latent space. Crucially, this approach circumvents the N -representability problem, as the learned manifold implicitly restricts the optimization to physically valid quantities.

Authors 3

1. Felix Frohnert Aachen

   Leiden University

   Affiliation as printed

   Universiteit Leiden

2. Emiel Koridon Aachen

   Leiden University

   Affiliation as printed

   Universiteit Leiden

3. Stefano Polla Aachen

   Leiden University

   Affiliation as printed

   Universiteit Leiden