  Experimental quest for the hypothetical "quantum spin liquid" state has
recently met a few promising candidate materials including organic salts
\kappa-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, S=1/2 triangular-lattice
Heisenberg antiferromagnets consisting of molecular dimers. These compounds
exhibit no magnetic ordering nor the spin freezing down to very low
temperature, while various physical quantities exhibit gapless behaviors.
Recent dielectric measurements revealed the glassy dielectric response
suggesting the random freezing of the electric polarization degrees of freedom.
Inspired by this observation, we propose as a minimal model of the observed
quantum spin-liquid behavior the S=1/2 antiferromagnetic Heisenberg on the
triangular lattice with a quenched randomness in the exchange interaction. We
study both zero- and finite-temperature properties of the model by an exact
diagonalization method, to find that when the randomness exceeds a critical
value the model exhibits a quantum spin-liquid ground state. This
randomness-induced quantum spin-liquid state exhibits gapless behaviors
including the temperature-linear specific heat. The results provide a
consistent explanation of the recent experimental observations on organic
salts.
