Which Fermi-Hubbard models are simulated by 3x3 and 4x4 phosphorus arrays in silicon?

Recent studies report quantum simulations of the Fermi-Hubbard model in dopant-based silicon devices, demonstrating quantum control on system properties through the geometry, number, and distribution of dopants in the silicon matrix. The device's electronic structure determines which Fermi-Hubbard model will be simulated. This talk presents a detailed study of the Fermi-Hubbard model parameters for 3x3 and 4x4 phosphorus arrays in silicon, that can be extracted from all-atom tight-binding configuration-interaction electronic structure calculations. Our approach considers the dynamical evolution of localized electrons in the P array and extracts onsite, tunneling, coulomb, and exchange energies for the Fermi-Hubbard model that best matches the tight-binding results. As a function of dopant separation, our results reveal that electron tunneling beyond nearest-neighbors is an essential feature and that Hamiltonian parameters are sensitive to the electron number in the system. We also investigate the multielectron spin structure in these P-arrays, revealing the different roles that corner, face, and inner dopants play in determining the electron distribution and total spin.