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1T-TaS$_2$ is a cluster Mott insulator on the triangular lattice with 13 Taatoms forming a star of David cluster as the unit cell. We derive a twodimensional XXZ spin-1/2 model with four-spin ring exchange term to describethe effective low energy physics of a monolayer 1T-TaS$_2$, where the effectivespin-1/2 degrees of freedom arises from the Kramers degenerate spin-orbitalstates on each star of David. A large scale density matrix renormalizationgroup simulation is further performed on this effective model and we find agapless spin liquid phase with spinon Fermi surface at moderate to largestrength region of four-spin ring exchange term. All peaks in the static spinstructure factor are found to be located on the "$2k_F$" surface of half-filledspinon on the triangular lattice. Experiments to detect the spinon Fermisurface phase in 1T-TaS$_2$ are discussed.

Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T-TaS$_2$