A possible system to realize the spin chain Hamiltonian of equation (1) is a cold ensemble of N strongly interacting atoms in a one-dimensional trap of appropriate geometry33343536. Recent experiments have confirmed that spin chains may indeed be realized this way37 with tunable microscopic optical traps38. An outline of the procedure to map this system onto the Heisenberg XXZ spin model is presented in Supplementary Note 4. A pair of suitable internal atomic states can serve as the spin-up and spin-down states, with the microwave or radiofrequency transition frequency further tunable through a global magnetic field inducing spatially-uniform Zeeman shifts and by tightly focused non-resonant laser beams inducing site-selective ac Stark shifts 3139. In the full model, the strong contact interactions between the atoms are described by the dimensionless coefficients >>1 and g↑↑=g↓↓=κg, where the parameter κ>0 is related to the asymmetry parameter of the effective Heisenberg spin- model as . In turn, the exchange constants of the Heisenberg model are proportional to the geometric factors αj which are determined by the single particle solutions of the Schrödinger equation in a one-dimensional confining potential V(x). Hence, the shape of the trapping potential can be used to tune the necessary parameters of the effective spin chain34.