Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ 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 sizeable region of the phase diagram. This topological phase is situated in between a coplanar $120^\circ$ N\'{e}el ordered and a non-coplanar tetrahedrally ordered phase. Furthermore we discuss the nature of the spin-disordered intermediate phase in the $J_1$-$J_2$ model. We compare the groundstates from Exact Diagonalization with a Dirac spin liquid wavefunction and propose a scenario where this wavefunction describes the quantum critical point between the $120^\circ$ magnetically ordered phase and a putative $\mathbb{Z}_2$ spin liquid.