Quantum spin liquids (QSLs) are fluid-like states of quantum spins where its long-range ordered state is destroyed by quantum fluctuations. The ground state of QSL and its exotic phenomena, which have been extensively discussed for decades, have yet to be identified. We employ thermal transport measurements on newly discovered QSL candidates, $kappa$-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, and report that the two organic insulators possess different QSLs characterized by different elementary excitations. In $kappa$-(BEDT-TTF)2Cu2(CN)3, heat transport is thermally activated at low temperatures, suggesting presence of a spin gap in this QSL. In stark contrast, in EtMe3Sb[Pd(dmit)2]2, a sizable linear temperature dependence of thermal conductivity is clearly resolved in the zero-temperature limit, showing gapless excitation with a long mean free path (~1,000 lattice distances). Such a long mean free path demonstrates a novel feature of QSL as a quantum-condensed state with long-distance coherence.
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