Monte Carlo simulations based on the Trotter-Suzuki transformation were carried out using 6 × 6 and 12 × 12 lattices and the single-band Hubbard model with intermediate-range repulsive interaction. The absence of the "minus-sign problem" for sufficiently low temperatures and appropriate doping indicates bosonic behavior reminiscent of superconductivity. It was found that holes prefer to pair on next-nearest-neighbor sites while nearest neighbors are suppressed. Additional electron-phonon coupling in the form of the breathing mode not only preserves this symmetry but strengthening of the bosonic background indicates the possibility of superconductivity.
