Year: 2026
Type: article
Abstract: Excited states play a central role in determining the physical properties of quantum matter, yet their accurate computation in many-body systems remains a formidable challenge for numerical methods. While neural quantum states have delivered outstanding results for ground-state problems, extending their applicability to excited states has faced limitations, including instability in dense spectra and reliance on symmetry constraints or penalty-based formulations. In this work, we rigorously formalize the framework introduced by Pfau et al.~\cite{pfau2024accurate} in terms of Grassmann geometry of the Hilbert space. This allows us to generalize the Stochastic Reconfiguration method for the simultaneous optimization of multiple variational wave functions, and to introduce the multidimensional versions of operator variances and overlaps. We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
DOI: 10.1103/l8mr-567g
Institution: École Polytechnique Fédérale de Lausanne
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170659453