Sign-Free Determinant Quantum Monte Carlo Study of the Bilayer Hubbard and Two-Orbital Hubbard-Kanamori Models

Two-band Hubbard models, as prototypes for various strongly correlated systems, have attracted intense research interest over the past few decades. Determinant Quantum Monte Carlo (DQMC), an unbiased finite-temperature numerical technique well suited to study such models, generically suffers from the fermion sign problem. However, for some variations, e.g. the bilayer Hubbard model with symmetric electron-hole doping and the half-filled two-orbital Hubbard-Kanamori model, particle-hole symmetry can be utilized to perform sign-problem-free studies. Here, using DQMC we show that the bilayer Hubbard model possesses a Berezinskii–Kosterlitz–Thouless (BKT) transition to an inter-layer biexciton condensate at intermediate coupling and finite electron-hole doping. For the Hubbard-Kanamori model, we treat the full rotationally invariant interaction, including the Hubbard and Hund’s coupling terms, using a decoupling scheme which involves a 12-state auxiliary field per site, and present the magnetic correlation and phase transition results obtained from DQMC.