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TT: Fachverband Tiefe Temperaturen
TT 7: Correlated Electrons: Electronic Structure Calculations
TT 7.6: Talk
Monday, March 18, 2024, 10:45–11:00, H 3025
Neural-network-boosted exact diagonalization: A new approach and a new community code — •Pavlo Bilous1, Louis Thirion2, and Philipp Hansmann2 — 1Max Planck Institute for the Science of Light, Staudtstr. 2, 91058 Erlangen, Germany — 2Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
The solution of quantum many-body systems (clusters) in truncated finite size Hilbert spaces presents a paradigm in many fields of research ranging from quantum chemistry to condensed matter physics. Whether the considered clusters are of real nature (atoms, molecules) or auxiliary (e.g. as used in dynamical mean-field theory), solving the eigenvalue equation for the Hamiltonian Ĥ Ψ = E Ψ with exact or numerical diagonalization procedures is severely limited due to the exponential growth of the Hilbert space dimension w. r. t. the single particle quantum numbers (orbitals/sites). However, it turns out that often only a small subset of basis states is sufficient to approximate expectation values of observables. The challenge is to identify this a priori unknown subset: In this talk we present an approach to converge observables like the ground state energy with successive basis extension and basis selection steps which are assisted by a neural-network (NN) classification scheme. Concrete examples show that the NN selection outperforms traditional truncation schemes dramatically and might push the boundaries of such calculations by an order of magnitude. The method is integrated in SOLAX: a new JAX-based parallelized GPU-accelerated Python code which we are currently developing.
Keywords: Many-body problem; Exact diaginalization; Neural networks; Machine learning; JAX