Dopant arrays in Si as quantum simulators of magnetic field effects

Atomically precise fabrication of dopant arrays in Si provides exciting opportunities to perform quantum simulations and study the dynamics of engineered quantum systems. We describe theoretical simulations done for two-dimensional arrays of dopants in Si in a magnetic field. An extended range Fermi-Hubbard model with a magnetic field is studied. Theoretical simulations are done for a range of magnetic fields, as a function of the electron-electron interaction to test the limits of weak and strong interaction. 2x2 arrays are considered to show the effects of magnetic field on interacting electrons when there is a single plaquette. Recent quantum-dot experiments have shown that Nagaoka ferromagnetism can be realized in these structures. 3x3 dopant arrays are also studied theoretically as an example of magnetic field effects when there are four connected plaquettes. Experiments on 3x3 dopant structures have been recently started at NIST. Time-dependent studies of these arrays have been developed to model the evolution of the local charge distribution in the array during transport. Results will be presented with and without a magnetic field to show how the magnetic field changes the local transport of charge through an array with interacting electrons.