Chiral spin liquid and quantum criticality in extended S=12 Heisenberg models on the triangular lattice

We investigate the $J_1-J_2$ Heisenberg model on the triangular lattice with an additional scalar chirality term and show that a chiral spin liquid is stabilized in a sizable region of the phase diagram. This topological phase is situated in between a coplanar ${120}^{\circ }$ Néel ordered and a noncoplanar tetrahedrally ordered phase. Furthermore we discuss the nature of the spin-disordered intermediate phase in the $J_1-J_2$ model. We compare the ground states from exact diagonalization with a Dirac spin liquid wave function and propose a scenario where this wave function describes the quantum critical point between the ${120}^{\circ }$ magnetically ordered phase and a putative ${\mathbb{Z}}_2$ spin liquid.