  Strongly enhanced quantum fluctuations often lead to a rich variety of
quantum-disordered states. A representative case is liquid helium, in which
zero-point vibrations of the helium atoms prevent its solidification at low
temperatures. A similar behaviour is found for the internal degrees of freedom
in electrons. Among the most prominent is a quantum spin liquid (QSL), in which
localized spins are highly correlated but fluctuate even at absolute zero.
Recently, a coupling of spins with other degrees of freedom has been proposed
as an innovative approach to generate even more fascinating QSLs such as
orbital--spin liquids. However, such ideas are limited to the internal degrees
of freedom in electrons. Here, we demonstrate that a coupling of localized
spins with the zero-point motion of hydrogen atoms (proton fluctuations) in a
hydrogen-bonded organic Mott insulator provides a new class of QSLs. We find
that a divergent dielectric behaviour towards a hydrogen-bond order is
suppressed by the quantum proton fluctuations, resulting in a quantum
paraelectric (QPE) state. Furthermore, our thermal-transport measurements
reveal that a QSL state with gapless spin excitations rapidly emerges upon
entering the QPE state. These findings indicate that the quantum proton
fluctuations give rise to a novel QSL --- a quantum-disordered state of
magnetic and electric dipoles --- through the coupling between the electron and
proton degrees of freedom.
