For many decades physicists have been searching for "hot'' enough playgrounds that can melt magnetic freezing even at extremely low temperatures, purely due to strong quantum fluctuations. The resulting quantum paramagnetic phases of matter called spin liquids, do not spontaneously break any symmetries, possess quantum and topological orders, and consequently fall outside the paradigm of traditional condensed matter theory based on the Landau's Fermi liquid theory and Landau's theory of phase transitions. Remarkably enough, the "deceptively'' simple spin-1/2 Heisenberg antiferromagnetic model, when put on the most frustrated lattice, the "kagome'' lattice, has been shown, both experimentally and theoretically to host such an exotic state. I will present my research work dealing with the precise identification of this state, which is currently being debated very intensely. I will show, within fermionic slave particle approaches, that a certain "marginally'' stable spin liquid with a U(1) low energy gauge structure (so-called Dirac spin liquid) is remarkably robust to all known perturbations towards stable Z2 spin liquids and Valence-bond crystals, despite having strongly interacting gapless fermionic excitations down to zero energy. Finally, using state-of-the-art numerical techniques such as the application of Lanczos steps on variational wave functions combined with Green's function Monte Carlo technique, I will show that such an exotic algebraic spin liquid can in fact exist as a real physical spin liquid ground state. PUBLICATIONS: 1.) Phys. Rev. B 83, 100404 (2011) - Y. Iqbal, F. Becca, and D. Poilblanc. 2.) Phys. Rev. B 84, 020407 (2011) (Editor's suggestion) - Y. Iqbal, F. Becca, and D. Poilblanc. 3.) New J. Phys 14, (in press) (2012); arXiv: 1203.3421 - Y. Iqbal, F. Becca, and D. Poilblanc. 4.) arXiv: 1209.1858 [cond.mat] (2012) - Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc.