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Organic solids host various electronic phases. Especially, a milestonecompound of organic solid, $\beta'$-$X$[Pd(dmit)$_2$]$_2$ with $X$=EtMe$_3$Sbshows quantum spin-liquid (QSL) properties suggesting a novel state of matter.However, nature of the QSL has been largely unknown. Here, we computationallystudy five compounds comprehensively with different $X$ using 2D $ab$ $initio$Hamiltonians and correctly reproduce experimental phase diagram withantiferromagnetic order for $X$=Me$_4$P, Me$_4$As, Me$_4$Sb, Et$_2$Me$_2$As anda QSL for $X$=EtMe$_3$Sb without adjustable parameters. We find that the QSLfor $X$=EtMe$_3$Sb exhibits 1D nature characterized by algebraic decay of spincorrelation along one direction, while exponential decay in the otherdirection, indicating dimensional reduction from 2D to 1D. The 1D nature indeedaccounts for the experimental specific heat, thermal conductivity and magneticsusceptibility. The identified QSL, however, preserves 2D nature as wellconsistently with spin fractionalization into spinon with Dirac-like gaplessexcitations and reveals duality bridging the 1D and 2D QSLs.

Unconventional dual 1D-2D quantum spin liquid revealed by $ab$ $initio$ studies on organic solids family