  Using determinant quantum Monte Carlo (d-QMC) simulations, we demonstrate
that an extended Hubbard model on a bilayer honeycomb lattice has two novel
quantum phase transitions. The first is a quantum phase transition between the
weakly interacting gapless Dirac fermion phase and a strongly interacting fully
gapped and symmetric trivial phase, which cannot be described by the standard
Gross-Neveu model. The second is a quantum critical point between a quantum
spin Hall insulator with spin $S^z$ conservation and the previously mentioned
strongly interacting fully gapped phase. At the latter quantum critical point
the single particle excitations remain gapped, while spin and charge gap both
close. We argue that the first quantum phase transition is related to the
$\mathbb{Z}_{16}$ classification of the topological superconductor
$^3\text{He-B}$ phase with interactions, while the second quantum phase
transition is a topological phase transition described by a bosonic O(4)
nonlinear sigma model field theory with a $\Theta$-term.
