Ground state and excitation properties of the quantum kagom\'{e} system ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ investigated by local probes.

We present a comprehensive study on the ground state and excitation spectrum of the $S=1/2$, analytically pure and perfect kagom\'{e} system ZnCu$_{3}$% (OH)$_{6}$Cl$_{2}$ using the following measurements: magnetization, muon spin rotation frequency shift $K$, transverse relaxation time $T_{2}^{\ast }$% , and zero field relaxation, and Cl nuclear spin-lattice relaxation $T_{1}$. Using our data we address four questions which are at the heart of the investigation of the quantum kagom\'{e} system: Do $S=1/2$ spins on kagom% \'{e} lattice freeze? Is the ground state magnetic? What is the density of excited states, and is there a gap in the spin energy spectra? Finally, does the lattice distort in order to accommodate spin-Peierls state? We found no sign of singlet formation, no long range order nor spin freezing, and no sign of spin-Peierls transition even at temperatures as low as $60$~mK. The density of states has an $E^{1/4}$ energy dependence with a negligible magnetic gap to excitation. Thus ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ is an exotic magnet with no broken continuous symmetry but gapless excitations.