  A quantum spin liquid (QSL) is a state of matter in which magnetic spins
interact strongly, but quantum fluctuations inhibit long-range magnetic order
even at zero temperature. A QSL has been predicted to have a host of exotic
properties, including fractionalized excitations and long-range quantum
entanglement. Despite the numerous theoretical studies, experimental
realization of a QSL has proved to be challenging due to the lack of candidate
materials. The triangular organic salts EtMe3Sb[Pd(dmit)2]2 and
{\kappa}-(BEDT-TTF)2Cu2(CN)3, and kagome ZnCu3(OH)6Cl2 (Herbertsmithite) have
recently emerged as promising candidates of exhibiting a QSL state, but the
nature of their ground states is still elusive. Here we studied a large-area
high-quality single crystal of Herbertsmithite by means of time-domain
terahertz (THz) spectroscopy. We observed in the low-frequency (0.6-2.2 THz)
optical conductivity evidence for the nature of the spin system. In particular,
the in-plane absorption spectrum exhibits a unique frequency dependence that
can be described by a power-law with an exponent of approximately 1.4, in sharp
contrast with the {\omega}^4 dependence expected for an ordered Mott insulator.
The absorption is also found to increase as the temperature decreases, a
behavior unexpected for conventional insulators. Such features are consistent
with recent theory based on the interactions between the charge and spin
degrees of freedom in a QSL system.
