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We carry out a sign-problem-free quantum Monte Carlo calculation of a bilayermodel with a repulsive intra-layer Hubbard interaction and a ferromagneticinter-layer interaction. The latter breaks the global $SU(2)$ spin rotationalsymmetry but preserves a $U(2)\times U(2)$ invariance under mixing of same-spinelectrons between layers. We show that despite the difference in symmetry, thebilayer model exhibits the same qualitative features found in the single-layerHubbard model. These include stripe phases, whose nature is sensitive to thepresence of next-nearest-neighbor hopping, a maximum in the Knight shift thatmoves to lower temperatures with increasing hole doping, and lack of evidencefor intra-layer d-wave superconductivity. Instead, we find a superconductingphase, coexisting with stripes, whose critical temperature traces a dome as afunction of doping and is due to inter-layer spin-polarized pairing that isinduced by the ferromagnetic interaction.

Quantum Monte Carlo study of a bilayer $U(2)\times U(2)$ symmetric Hubbard model