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Topological phase separation in 2D hard-core Bose-Hubbard system away from half-filling

We suppose that the doping of the 2D hard-core boson system away from half-filling may result in the formation of multi-center topological defect such as charge order (CO) bubble domain(s) with Bose superfluid (BS) and extra bosons both localized in domain wall(s), or a {\it topological} CO+BS {\it phase separation}, rather than an uniform mixed CO+BS supersolid phase. Starting from the classical model we predict the properties of the respective quantum system. The long-wavelength behavior of the system is believed to remind that of granular superconductors, CDW materials, Wigner crystals, and multi-skyrmion system akin in a quantum Hall ferromagnetic state of a 2D electron gas.