  We propose a model with quantum bosons on the fcc lattice, which has a stable
algebraic Bose liquid phase at low energy. We show that this phase is described
by emergent quantum gravity at the Gaussian z = 3 Lifshitz fixed point in 3+1
dimensions. The stability of this algebraic Bose liquid phase is guaranteed by
the gauge symmetry of gravitons and self-duality of the low energy field
theory. By tuning one parameter in the lattice boson model we can drive a phase
transition between the z = 3 Lifshitz gravity and another algebraic Bose liquid
phase, described by gravity at the z = 2 Lifshitz point.
