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We study the quantum phase transition between the $Z_2$ spin liquid andvalence bond solid (VBS) orders on a triangular lattice. With a fully isotropictriangular lattice, the transition from a columnar or resonating-plaquette VBSorder can be either first order or there could be two transitions with anintermediate phase. If the transition splits into two, then the $Z_2$ spinliquid will first experience a first order $q=3$ Potts transition to a newnematic $Z_2$ spin liquid that breaks the $2\pi/3$ lattice rotation symmetry(but retain translation symmetry unlike the VBS states). The second transitionwill then take this new nematic $Z_2$ spin liquid to a columnar orresonating-plaquette VBS state through a second order $3d$ XY$^*$ transition.On a distorted triangular lattice, the degeneracy between some of the differentcolumnar VBS orders is lifted, and the phase transition can reduce to a single$3d$ XY$^*$ transition.

Quantum Phase Transition between Z2 spin liquid and columnar Valence Bond Crystals on a Triangular lattice