Organic solids host various electronic phases. Especially, a milestone compound of organic solid, β′-X[Pd(dmit)2]2 with X=EtMe3Sb shows quantum spin-liquid (QSL) properties suggesting a novel state of matter. However, the nature of the QSL has been largely unknown. Here, we computationally study five compounds comprehensively with different X using 2D ab initio Hamiltonians and correctly reproduce the experimental phase diagram with antiferromagnetic order for X=Me4P, Me4As, Me4Sb, Et2Me2As and a QSL for X=EtMe3Sb without adjustable parameters. We find that the QSL for X=EtMe3Sb exhibits 1D nature characterized by algebraic decay of spin correlation along one direction, while exponential decay in the other direction, indicating dimensional reduction from 2D to 1D. The 1D nature indeed accounts for the experimental specific heat, thermal conductivity and magnetic susceptibility. The identified QSL, however, preserves 2D nature as well consistently with spin fractionalization into spinon with Dirac-like gapless excitations and reveals duality bridging the 1D and 2D QSLs.
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