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Inspired by recent experiments on bilayer 3He, we consider a bilayer Hubbardmodel on a triangular lattice. For appropriate model parameters, we observe aband-selective Mott transition at a critical chemical potential, mu_c,corresponding to the solidification of the fermions in the first layer. Thegrowth of the effective mass on the metallic side (mu < mu_c) is cut off by afirst order transition in which the first layer fermions drop out of theLuttinger volume and their spin degrees of freedom become locked in a spinsinglet state. These results are obtained from a cluster dynamical mean-fieldcalculation on an eight-site cluster with a quantum Monte Carlo cluster solver.

Bilayer Hubbard model for 3He: a cluster dynamical mean-field calculation