Two-particle pairing and phase separation in a two-dimensional Bose gas with one or two sorts of bosons

We present a phase diagram for a dilute two-dimensional Bose gas on a lattice. For one sort of boson we consider a realistic case of the van der Waals interaction between particles with a strong hard-core repulsion U and a van der Waals attractive tail V. For V<2t, t being a hopping amplitude, the phase diagram of the system contains regions of usual one-particle Bose-Einstein condensation (BEC). However for V>2t we have total phase separation on a Mott-Hubbard Bose solid and a dilute Bose gas. For two sorts of structureless bosons described by the two-band Hubbard model, an s-wave pairing of the two bosons of different sort not equal0 is possible. The results we obtained should be important for different Bose systems, including submonolayers of He-4, excitons in semiconductors, Schwinger bosons in magnetic systems and holons in HTSC. In the HTSC case a possibility of two-holon pairing in the slave-boson theories of superconductivity can restore a required charge 2e of a Cooper pair.