Low-energy spin systems based on the Bernasconi model

A method of constructing a low-level quantum system for a one-dimensional spin lattice consisting of N particles is proposed. In the Bernasconi model, the problem of constructing the simplest quantum system in the form of a one-dimensional Ising model reduces to the problem of constructing binary sequences with the lowest side-lobe energy. In this paper, we provide a computationally effective method of exhaustive search for binary sequences with a low level of side lobes. Examples of low-level one-dimensional spin lattices of record lengths N > 80 are synthesized and presented