Abstract
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 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 for any value of U and a band insulator at large . At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small 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 in the range of . Finally, we discuss the phase diagrams obtained in relation to findings from previous studies based on different many-body approaches.
Highlights
Understanding the origin of transitions from a metal to a Mott or a band insulator in correlated systems has been a topic of intensive debate in the past few years
Our results suggest that the Mott insulator to band insulator transition is of first order in the non-magnetic phase diagram, while it becomes continuous when magnetic order is allowed
Comparison of our results to the ones obtained with dynamical mean-field theory (DMFT) [8] and cluster DMFT [9] reveals that our non-magnetic phase diagram includes some features observed in DMFT and 2 × 2 cluster DMFT and new distinct properties, as follows
Summary
Understanding the origin of transitions from a metal to a Mott or a band insulator in correlated systems has been a topic of intensive debate in the past few years. Various generalizations of the Hubbard model have been investigated for this purpose, like the extended Hubbard model [1], the ionic Hubbard model in one and two dimensions [2,3,4,5,6], the two-band Hubbard model [7] and the bilayer Hubbard model [8,9,10,11,12,13,14,15]. With this study (i) we are able to resolve some discrepancies between previous DMFT and cluster DMFT studies and (ii) we find new aspects of the Mott to band transition not captured in previous studies
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