  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.
