  The nontrivialness of quantum spin liquid (QSL) typically manifests in the
non-local observables that signifies their existence, however, this fact
actually casts shadow on detecting QSL with experimentally accessible probes.
Here, we provide a solution by unbiasedly demonstrating dynamical signature of
anyonic excitations and symmetry fractionalization in QSL. Employing
large-scale quantum Monte Carlo simulation and stochastic analytic
continuation, we investigate the extended XXZ model on the kagome lattice, and
find out that across the phase transitions from Z2 QSLs to different symmetry
breaking phases, spin spectral functions can reveal the presence and
condensation of emergent anyonic spinon and vison excitations, in particular
the translational symmetry fractionalization of the latter, which can be served
as the unique dynamical signature of the seemingly ephemeral QSLs in
spectroscopic techniques such as inelastic neutron or resonance (inelastic)
X-ray scatterings.
