  Antiferromagnetic Heisenberg model on the triangular lattice is perhaps the
best known example of frustrated magnets, but it orders at low temperatures.
Recent density matrix renormalization group (DMRG) calculations find that next
nearest neighbor interaction $J_2$ enhances the frustration and leads to a spin
liquid for $J_2/J_1\in (0.08,0.15)$. In addition, DMRG study of a dipolar
Heisenberg model with longer range interactions gives evidence for a spin
liquid at small dipole titling angle $\theta\in[0,10^\circ)$. In both cases,
the putative spin liquid region appears to be small. Here, we show that for the
triangular lattice dipolar Heisenberg model, a robust quantum paramagnetic
phase exists in a surprisingly wide region, $\theta\in [0,54^\circ)$, for
dipoles tilted along the lattice diagonal direction. We obtain the phase
diagram of the model by functional renormalization group (RG) which treats all
magnetic instabilities on equal footing. The quantum paramagnetic phase is
characterized by a smooth continuous flow of vertex functions and spin
susceptibility down to the lowest RG scale, in contrast to the apparent
breakdown of RG flow in phases with stripe or spiral order. Our finding points
to a promising direction to search for quantum spin liquids in ultracold
dipolar molecules.
