Grassmann Variational Monte Carlo with neural wave functions

• URL: http://arxiv.org/abs/2507.10287v1
• Date: Mon, 14 Jul 2025 13:53:13 GMT
• Title: Grassmann Variational Monte Carlo with neural wave functions
• Authors: Douglas Hendry, Alessandro Sinibaldi, Giuseppe Carleo,
• Abstract summary: We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>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.
• Score: 45.935798913942904
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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