Spinon-Phonon Interaction in Algebraic Spin Liquids

Motivated by a search for experimental probes to access the physics of fractionalized excitations called spinons in a spin liquids, we study the interaction of spinons with lattice vibrations. We consider the case of algebraic spin liquid, when spinons have fermionic statistics and a Dirac-like dispersion. We establish the general procedure for deriving spinon-phonon interactions which is based on a symmetry considerations. The procedure is illustrated for four different algebraic spin liquids: pi-flux and staggered-flux phases on a square lattice, pi-flux phase on a kagome lattice, and zero flux phase on a honeycomb lattice. Although the low energy description is similar for all these phases, different underlying symmetry group leads to a distinct form of spinon-phonon interaction Hamiltonian. The explicit form of the spinon-phonon interaction is used to estimate the attenuation of ultrasound in an algebraic spin liquid. The perspectives of the sound attenuation as probe of spinons are discussed.