“…Combination of these two apparently antithetical properties has attracted the attentions of both experimentalists and theorists, and searching for this phase has become one of the main subjects of condensed matter and cold atoms physics [5,6,7,8,9,10,11,12]. An appropriate ground for searching various supersolid phases are quantum spin systems [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]. Recently it has been shown experimentally that mixed-spin systems, composed of two kinds of spin, display various supersolid phases in their ground state phase diagrams [35,36].…”