We present the first variational Monte Carlo study of nuclear and hypernuclear excited states within the neural-network quantum states (NQS) framework. We implement both the overlap penalty (OP) and natural excited state (NES) methods to compute low-lying excitation spectra. To address the spin contamination in hypernuclear calculations, we propose a quantum number targeting (QNT) technique for the OP method. Both the OP-QNT and NES methods can reproduce diagonal observables, such as energies and spatial structures, in excellent agreement with rigorous benchmarks. We further provide, to our knowledge, the first ab initio calculation of the M 1 transition strength for Λ 4 H . The calculated transition strength is consistent with the weak-coupling limit, exhibiting a ∼ 1.3% suppression. This work demonstrates that NQS can be elevated from ground-state solvers to practical tools for nuclear and hypernuclear spectroscopy.
We present the first variational Monte Carlo study of nuclear and hypernuclear excited states within the neural-network quantum states (NQS) framework. We implement both the overlap penalty (OP) and natural excited state (NES) methods to compute low-lying excitation spectra. To address the spin contamination in hypernuclear calculations, we propose a quantum number targeting (QNT) technique for the OP method. Both the OP-QNT and NES methods can reproduce diagonal observables, such as energies and spatial structures, in excellent agreement with rigorous benchmarks. We further provide, to our knowledge, the first ab initio calculation of the M 1 transition strength for Λ 4 H . The calculated transition strength is consistent with the weak-coupling limit, exhibiting a ∼ 1.3% suppression. This work demonstrates that NQS can be elevated from ground-state solvers to practical tools for nuclear and hypernuclear spectroscopy.
A thorough description of baryonic system beyond first-generation quark sector is indispensable for the maturation of nuclear ab initio methods. This study pioneers the application of neural-network quantum states to hypernuclei, with trainable parameters determined by variational Monte Carlo approach (VMC-NQS). In order to reduce the numerical uncertainty and treat the nucleons and hyperons in a unified manner, spinor grouping (SG) method is proposed to analytically integrate out isospin degrees of freedom. With SG method and spin symmetry enforcement, the Λ separation energies of s -shell hypernuclei are computed with one-thousandth level accuracy and benchmarked against existing results from stochastic variational method, showing superior performance. By comparing two different sets of Hamiltonian based on pionless effective field theory ( π ̸ EFT), we choose an optimal model and further carry out calculations of selected p -shell charge-symmetric hypernuclei with mass number up to 13, exhibiting satisfactory consistency with experimental results. Our work underscores the potential of the VMC-NQS family for the in-depth probing of hypernuclear systems.
This study explores the application of neural network variational Monte Carlo (NN-VMC) for the computation of low-lying excited states in molecular systems. Our focus lies on the implementation and evaluation of two distinct methodologies, the penalty method and a novel modification of the auxiliary wave function (AW) method, within the framework of the FermiNet-based NN-VMC package. Importantly, this specific application has not been previously reported.Our investigation advocates for the efficacy of the modified AW method, emphasizing its superior robustness when compared to the penalty method. This methodological advancement introduces a valuable tool for the scientific community, offering a distinctive approach to target low-lying excited states. We anticipate that the modified AW method will garner interest within the research community, serving as a complementary and robust alternative to existing techniques. Moreover, this contribution enriches the ongoing development of various neural network ansatz, further expanding the toolkit available for the accurate exploration of excited states in molecular systems.
We present an algorithm to estimate the excited states of a quantum system by variational Monte Carlo, which has no free parameters and requires no orthogonalization of the states, instead transforming the problem into that of finding the ground state of an expanded system. Arbitrary observables can be calculated, including off-diagonal expectations, such as the transition dipole moment. The method works particularly well with neural network ansätze, and by combining this method with the FermiNet and Psiformer ansätze, we can accurately recover excitation energies and oscillator strengths on a range of molecules. We achieve accurate vertical excitation energies on benzene-scale molecules, including challenging double excitations. Beyond the examples presented in this work, we expect that this technique will be of interest for atomic, nuclear, and condensed matter physics.
An efficient emulator for \emph{ab initio} calculations of nuclear ground-state properties is developed by integrating the neural-network variational Monte Carlo framework, FeynmanNet, with the eigenvector continuation. It enables the calculation of observables for different Hamiltonians with minimal computational cost, while delivering ground-state energies with errors below 0.5% compared to the full FeynmanNet results. With this emulator, the ground-state energies and charge radii of 16O, 15O, 14O, 15N, and 14C are computed using a nuclear Hamiltonian derived from the leading-order pionless effective field theory, with a large number of different values of low-energy constants (LECs). Then, we perform a global sensitivity analysis of the ground-state energies, charge radii, separation energies of selected nuclei for the three LECs in the Hamiltonian, to identify how each LEC contributes to the variances of these observables. It shows that the two-body LEC in the 3S1 channel is the most influential LEC governing these nuclear bulk properties. Finally, the correlations among the ground-state energies of 4He, 12C, and 16O are investigated by varying the LECs in the Hamiltonian. The analysis reveals that the experimental ground-state energies of 12C and 16O cannot be reproduced simultaneously by varying the LECs in the leading-order pionless Hamiltonian. This suggests that additional ingredients in the leading-order Hamiltonian are required to improve its description of light nuclei. The present work establishes an efficient framework for global sensitivity analysis and uncertainty quantification in the quantum Monte Carlo calculations for light and medium-mass nuclei.
Predicting a nuclear magnetic resonance (NMR) spectrum from first principles requires propagating a quantum state of dimension 2N for N coupled spins, which becomes intractable beyond larger N. We benchmark Neural Quantum States (NQS), a class of variational quantum states expressed as an artificial neural network, as an alternative representation for this problem. Using two propagation methods, the Time-Dependent Variational Principle (TDVP) and projected time-dependent Variational Monte Carlo (p-tVMC), we compute the 1H spectra of four (2→5 spins) experimentally parameterized molecules. TDVP reproduces all line positions and intensities with average spectral mean squared errors of <10−3; p-tVMC reproduces the same features, with accuracy determined by its per-step optimization parameters. One dominant obstacle to larger systems is the steep growth of the number of integration steps with spectral bandwidth, which can be removed by propagating in the interaction frame of the chemical-shifted Hamiltonian. Retaining the same accuracy, this reduces the number of integration steps roughly eightfold for the 3-spin system and by at least an order of magnitude for the 4- and 5-spin systems, and it enables a 14-spin molecule (sucrose) to be accurately propagated via Monte Carlo sampling.
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.