Neural quantum states for simulating strongly interacting fermions in continuous space

          @misc{ pirsa_PIRSA:23060032,
            doi = {10.48660/23060032},
            url = {https://pirsa.org/23060032},
            author = {},
            keywords = {Condensed Matter},
            language = {en},
            title = {Neural quantum states for simulating strongly interacting fermions in continuous space},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {jun},
            note = {PIRSA:23060032 see, \url{https://pirsa.org}}
          }
          

Abstract

ZOOM: https://pitp.zoom.us/j/94595394881?pwd=OUZSSXpzYlhFcGlIRm81Y3VaYVpCQT09 We introduce a novel neural quantum state architecture for the accurate simulation of extended, strongly interacting fermions in continuous space. The variational state is parameterized via permutation equivariant message passing neural networks to transform single-particle coordinates to highly correlated quasi-particle coordinates. We show the versatility and accuracy of this Ansatz by simulating the ground-state of the 3D homogeneous electron gas at different densities and system sizes. Our model respects basic symmetries of the Hamiltonian, such as continuous translation symmetries. We compare our ground-state energies to results obtained by different state-of-the-art NQS Ansaetze for continuous space, as well as to different quantum chemistry methods. We obtain better or comparable ground-state energies, while using orders of magnitudes less variational parameters and optimization steps. We investigate its capability of identifying and representing different phases of matter without imposing any structural bias toward a given phase. We scale up to system sizes of N=128 particles, opening the door for future work on finite-size extrapolations to the thermodynamic limit.