Sign-Alternating Interaction Mediated by Strongly-Correlated Lattice   Bosons
  We reveal a generic mechanism of generating sign-alternating inter-site interactions mediated by strongly correlated lattice bosons. The ground state phase diagram of the two-component hard-core Bose-Hubbard model on a square lattice at half-integer filling factor for each component, obtained by worm algorithm Monte Carlo simulations, is strongly modified by these interactions and features the solid+superfluid phase for strong anisotropy between the hopping amplitudes. The new phase is a direct consequence of the effective nearest-neighbor repulsion between "heavy" atoms mediated by the "light" superfluid component. Due to their sign-alternating character, mediated interactions lead to a rich variety of yet to be discovered quantum phases. quantum phases. 
\c{S}.G. S\"oyler, B. Capogrosso-Sansone, N.V. Prokof'ev, B.V.   Svistunov