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We report the thermodynamic and muon spin relaxation ($\mu$SR) evidences fora possible gapless spin liquid in Tm$_{3}$Sb$_{3}$Zn$_{2}$O$_{14}$, with therare-earth ions Tm$^{3+}$ forming a two-dimensional kagom\'{e} lattice. Weextract the magnetic specific heat of Tm$_{3}$Sb$_{3}$Zn$_{2}$O$_{14}$ bysubtracting the phonon contribution of the non-magnetic isostructural materialLa$_{3}$Sb$_{3}$Zn$_{2}$O$_{14}$. We obtain a clear linear-$T$ temperaturedependence of magnetic specific heat at low temperatures, with theheat-capacity coefficient $\gamma$ = 26.6(1) mJ mol-Tm$^{-1}$ K$^{-2}$ in thezero temperature limit. No long-range magnetic order was observed down to 0.35K in the heat capacity measurement. A broad hump around 9 K was observed in thezero field magnetic specific heat and is gradually suppressed in the magneticfields that also create a spin gap in the specific heat. The absence ofmagnetic order is further confirmed by the $\mu$SR measurement down to 20 mK.We find that the spin-lattice relaxation time remains constant down to thelowest temperatures. We point out that the physics inTm$_{3}$Sb$_{3}$Zn$_{2}$O$_{14}$ is fundamentally different from the Cu-basedherbertsmithite and propose spin liquid ground states with non-Kramers doubletson the kagom\'{e} lattice to account for the experimental results.

Possible gapless spin liquid in a rare-earth kagom\'{e} lattice magnet Tm$_{3}$Sb$_{3}$Zn$_{2}$O$_{14}$