Nodal structures and analytical properties of many-body wavefunctions for quantum Monte Carlo

Luboš Mitáš, Cody Melton, M. Chandler Bennett

Dario Bressanini, Pietro Cremaschi, Massimo Mella +1 more

William Freitas, Bruno Ricardi de Abreu, S. A. Vitiello

Simulating strongly correlated fermionic systems remains a fundamental challenge in quantum physics, largely due to the sign problem in quantum Monte Carlo (QMC) methods. We present a neural network-based variational Monte Carlo (NN-VMC) approach, leveraging a flexible neural network ansatz to represent the many-body wavefunction. Focusing on quantum dots with up to 30 electrons, we demonstrate that NN-VMC significantly reduces variational bias and achieves ground-state energies surpassing those of fixed-node diffusion Monte Carlo (DMC). A key feature is that the neural network adaptively learns and optimizes nodal structures during energy minimization. We provide qualitative insights into the nodal structure of fermionic wavefunctions by comparing the nodal structures generated by NN-VMC with those obtained from traditional trial functions. Additionally, we reveal spin-resolved radial distributions and electron density profiles, highlighting the versatility and accuracy of NN-VMC. This work underscores the potential of machine learning to advance quantum simulations and deepen our understanding of strongly correlated systems.

R. N. Barnett, William A. Lester

Freitas, William, B De Abreu, S. A. Vitiello

Simulating strongly correlated fermionic systems remains a fundamental challenge in quantum physics, largely due to the sign problem in quantum Monte Carlo (QMC) methods. We present a neural network-based variational Monte Carlo (NN-VMC) approach, leveraging a flexible neural network ansatz to represent the many-body wavefunction. Focusing on quantum dots with up to 30 electrons, we demonstrate that NN-VMC significantly reduces variational bias and achieves ground-state energies surpassing those of fixed-node diffusion Monte Carlo (DMC). A key feature is that the neural network adaptively learns and optimizes nodal structures during energy minimization. We provide qualitative insights into the nodal structure of fermionic wavefunctions by comparing the nodal structures generated by NN-VMC with those obtained from traditional trial functions. Additionally, we reveal spin-resolved radial distributions and electron density profiles, highlighting the versatility and accuracy of NN-VMC. This work underscores the potential of machine learning to advance quantum simulations and deepen our understanding of strongly correlated systems.

Arne Lüchow, Tony C Scott

Previously unknown quantities of a general trial wavefunction ϕ are derived, namely the measure of the splittings between the nodal hypersurfaces obtained from the Hamiltonian operation , the kinetic energy operation , and that of ϕ itself, which occur because ϕ is not the true wavefunction. Insight into the structure of the true nodes is also revealed. In particular, we establish a bound for the location of a node of the exact wavefunction with respect to the node of the trial wavefunction. The nodal structure is of particular interest for quantum Monte Carlo calculations (QMC) and also for assessing and optimizing a trial wavefunction.