  When quantum fluctuations destroy underlying long-range ordered states, novel
quantum states emerge. Spin-liquid (SL) states of frustrated quantum
antiferromagnets, in which highly-correlated spins keep to fluctuate down to
very low temperatures, are prominent examples of such quantum states. SL states
often exhibit exotic physical properties, but the precise nature of the
elementary excitations behind such phenomena remains entirely elusive. Here we
utilize thermal Hall measurements that can capture the unexplored property of
the elementary excitations in SL states, and report on the observation of
anomalous excitations that may unveil the unique features of the SL state. Our
principal finding is a negative thermal Hall conductivity (k_xy) which the
charge-neutral spin excitations in a gapless SL state of the two-dimensional
kagome insulator volborthite Cu_3V_2O_7(OH)_2 \cdot 2H_2O exhibit, in much the
same way in which charged electrons give rise to the conventional electric Hall
effect. We find that k_xy is absent in the high-temperature paramagnetic state
and develops upon entering the SL state in accordance with the growth of the
short-range spin correlations, demonstrating that k_xy is a key signature of
the elementary excitation formed in the SL state. These results suggest the
emergence of nontrivial elementary excitations in the gapless SL state which
feel the presence of fictitious magnetic flux, whose effective Lorentz force is
found to be less than 1/100 of that experienced by free electrons.
