  We study analytically and numerically the thermoelectric properties of a
chain of cold atoms with dipole-dipole interactions placed in an optical
periodic potential. At small potential amplitudes the chain slides freely that
corresponds to the Kolmogorov-Arnold-Moser phase of integrable curves of a
symplectic map. Above a certain critical amplitude the chain is pinned by the
lattice being in the cantori Aubry phase. We show that the Aubry phase is
characterized by exceptional thermoelectric properties with the figure of merit
ZT = 25 being ten times larger than the maximal value reached in material
science experiments. We show that this system is well accessible for
magneto-dipole cold atom experiments that opens new prospects for
investigations of thermoelectricity.
