Quantum spin liquid (QSL) is a novel state of matter with exotic excitations and was theoretically predicted to be realized most possibly in an S=1/2 kagome antiferromagnet. Experimentally searching for the candidate materials is a big challenge in condensed matter physics and only two such candidates were reported so far. Here we report the successful synthesis of a new spin-1/2 kagome antiferromagnet ZnCu3(OH)6SO4. No magnetic ordering is observed down to 50 mK, despite a moderately high Weiss temperature of {theta}W ~ -79 K. It strongly suggests that the material is a new QSL candidate. Most interestingly, the magnetic specific heat clearly exhibits linear behaviors in two low-temperature regions. Both behaviors exactly correspond to two temperature-independent susceptibilities. These consistently reveal a novel re-entrance phenomenon of gapless QSL state at the lowest temperatures. The findings provide new insights into QSL ground and excited states and will inspire new theoretical and experimental studies.
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