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Motivated by experiments on non-magnetic triangular-lattice Mott insulators,we study one candidate paramagnetic phase, the columnar dimer (or valence-bond)phase. We apply variants of the bond-operator theory to a dimerized andspatially anisotropic spin-1/2 Heisenberg model and determine itszero-temperature phase diagram and the spectrum of elementary tripletexcitations (triplons). Depending on model parameters, we find that the minimumof the triplon energy is located at either a commensurate or an incommensuratewavevector. Condensation of triplons at this commensurate-incommensuratetransition defines a quantum Lifshitz point, with effective dimensionalreduction which possibly leads to non-trivial paramagnetic (e.g. spin-liquid)states near the closing of the triplet gap. We also discuss the two-particledecay of high-energy triplons, and we comment on the relevance of our resultsfor the organic Mott insulator EtMe3P[Pd(dmit)2]2.

Triangular-lattice anisotropic dimerized Heisenberg antiferromagnet: Stability and excitations of the quantum paramagnetic phase