  An experiment demonstrating the quantum simulation of a spin-lattice
Hamiltonian is proposed. Dipolar interactions between nuclear spins in a solid
state lattice can be modulated by rapid radio-frequency pulses. In this way,
the effective Hamiltonian of the system can be brought to the form of an
antiferromagnetic Heisenberg model with long range interactions. Using a
semiconducting material with strong optical properties such as InP, cooling of
nuclear spins could be achieved by means of optical pumping. An additional
cooling stage is provided by adiabatic demagnetization in the rotating frame
(ADRF) down to a nuclear spin temperature at which we expect a phase transition
from a paramagnetic to antiferromagnetic phase. This phase transition could be
observed by probing the magnetic susceptibility of the spin-lattice. Our
calculations suggest that employing current optical pumping technology,
observation of this phase transition is within experimental reach.
