A Bernasconi model for constructing ground-state spin systems and optimal binary sequences

A Bernasconi model for a one-dimensional chain of quantum particles is considered. It is shown that searching for the ground state of such a quantum system is equivalent to searching for optimal binary sequences with minimum energy levels. The second criteria for the optimality of binary sequences with low levels of aperiodic autocorrelation is the minimax criterion, in which the peak level of side lobe (PSL) must be minimal. A review and new results regarding the construction of such binary sequences up to length N=82 are presented. (paper)