  In quantum simulation, many-body phenomena are probed in controllable quantum
systems. Recently, simulation of Bose-Hubbard Hamiltonians using cold atoms
revealed previously hidden local correlations. However, fermionic many-body
Hubbard phenomena such as unconventional superconductivity and spin liquids are
more difficult to simulate using cold atoms. To date the required single-site
measurements and cooling remain problematic, while only ensemble measurements
have been achieved. Here we simulate a two-site Hubbard Hamiltonian at low
effective temperatures with single-site resolution using subsurface dopants in
silicon. We measure quasiparticle tunneling maps of spin-resolved states with
atomic resolution, finding interference processes from which the entanglement
entropy and Hubbard interactions are quantified. Entanglement, determined by
spin and orbital degrees of freedom, increases with increasing covalent bond
length. We find separation-tunable Hubbard interaction strengths that are
suitable for simulating strongly correlated phenomena in larger arrays of
dopants, establishing dopants as a platform for quantum simulation of the
Hubbard model.
