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 interlayer hopping t_perp 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_perp for any value of U and a band insulator at large t_perp. At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small t_perp 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 reentrant Mott insulator to metal transition and metal to band insulator transition for increasing t_perp in the range of 5.5t < U < 7.5t. Finally, we discuss the obtained phase diagrams in relation to previous studies based on different many-body approaches.