Gapless excitations in the ground state of 1T-TaS$_2$

1T-TaS$_2$ is a layered transition metal dichalgeonide with a very rich phase diagram. At T=180K it undergoes a metal to Mott insulator transition. Mott insulators usually display anti-ferromagnetic ordering in the insulating phase but 1T-TaS$_2$ was never shown to order magnetically. In this letter we show that 1T-TaS$_2$ has a large paramagnetic contribution to the magnetic susceptibility but it does not show any sign of magnetic ordering or freezing down to 20mK, as probed by $\mu$SR, possibly indicating a quantum spin liquid ground state. Although 1T-TaS$_2$ exhibits a strong resistive behavior both in and out-of plane at low temperatures we find a linear term in the heat capacity suggesting the existence of a Fermi-surface, which has an anomalously strong magnetic field dependence.