Critical dynamics of singlet excitations in a frustrated spin system

We construct and analyze a frustrated quantum spin model with plaquette order, in which the low-energy dynamics is controlled by spin singlets. At a critical value of frustration the singlet spectrum becomes gapless, indicating a quantum transition to a phase with dimer order. The magnetic susceptibility has an activated form throughout the phase diagram, whereas the specific heat exhibits a rich structure and a power-law dependence on temperature at the quantum critical point. This generic behavior can be relevant to quantum antiferromagnets on Kagomé and pyrochlore lattices where (almost) all low-energy excitations are spin singlets, as well as to the ${\mathrm{CaV}}_4{\mathrm{O}}_9$ lattice and the strongly frustrated antiferromagnets ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5(\mathrm{Cl},\mathrm{Br}{)}_2$ and ${\mathrm{Li}}_2\mathrm{VO}(\mathrm{Si},\mathrm{Ge}){\mathrm{O}}_4.$