The phase diagram of the square lattice bilayer Hubbard model: a variational Monte Carlo study

We investigate the phase diagram of the square lattice bilayer Hubbard model at half-filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping t(perpendicular to). and on-site Coulomb repulsion U. With this study we resolve some discrepancies in previous calculations based on the dynamical mean-field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: an antiferromagnetic Mott insulator at small t(perpendicular to) for any value of U and a band insulator at large t(perpendicular to). At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small t(perpendicular to). a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing t(perpendicular to) in the range of 5.5t < U < 7.5t. Finally, we discuss the phase diagrams obtained in relation to findings from previous studies based on different many-body approaches.