  The challenge of simulating many-body models with analogue physical systems
requires both experimental precision and very low operational temperatures.
Atomically precise placement of dopants in Si permits the construction of
nanowires by design. We investigate the suitability of these interacting
electron systems as simulators of a fermionic extended Hubbard model on demand.
We describe the single particle wavefunctions as a Linear Combination of Dopant
Orbitals (LCDO). The electronic states are calculated within configuration
interaction (CI). Due to the peculiar oscillatory behavior of each basis
orbital, properties of these chains are strongly affected by the interdonor
distance $R_0$, in a non-monotonic way. Ground state (T=0K) properties such as
charge and spin correlations are shown to remain robust under temperatures up
to 4K for specific values of $R_0$. The robustness of the model against
disorder is also tested, allowing some fluctuation of the placement site around
the target position. We suggest that finite donor chains in Si may serve as an
analog simulator for strongly correlated model Hamiltonians. This simulator is,
in many ways, complementary to those based on cold atoms in optical
lattices---the trade-off between the tunability achievable in the latter and
the survival of correlation at higher operation temperatures for the former
suggests that both technologies are applicable for different regimes.
