Spin-lattice coupling in quantum spin liquids

We construct phenomenological theories to investigate spin-lattice coupling in quantum spin liquids (QSLs) by using gauge-invariance and strain tensor with lattice symmetries. In deconfined QSLs, it is shown that perturbative approaches are valid, and our theory is applied to U(1) QSLs with gapped fractionalized particles in quantum spin ices, so-called emergent Coulomb phases. We find characteristic decay rates of emergent photons and acoustic phonons under spin-lattice coupling. Namely, the decay rate of the photons contains the Boltzmann factor while the decay rate of the phonons is dominated by temperature independent contributions. The characteristic behaviors of decay rates may affect physical quantities such as thermal conductivity.