Optical Conductivity of Visons in Z_{2} Spin Liquids Close to a Valence Bond Solid Transition on the Kagome Lattice

Abstract

We consider Z2 spin liquids on the kagome lattice on the verge of a valence bond solid (VBS) transition, where vortex excitations carrying Z2 magnetic flux—so-called visons—condense. We show that these vison excitations can couple directly to the external electromagnetic field, even though they carry neither spin nor charge. This is possible via a magnetoelastic coupling mechanism recently identified. [Potter, Senthil, and Lee, arXiv:1301.3495; Hao, Phys. Rev. B 85, 174432 (2012)] For the case of transitions to a 36-site unit cell VBS state, the corresponding finite ac conductivity has a specific power-law frequency dependence, which is related to the crossover exponent of the quantum critical point. The visons’ contribution to the optical conductivity at transitions to VBS states with a 12-site unit cell vanishes, however.