1H NMR and static susceptibility measurements have been performed in an organic Mott insulator with a nearly isotropic triangular lattice, kappa-(BEDT-TTF)2Cu2(CN)(3), which is a model system of frustrated quantum spins. The static susceptibility is described by the spin S=1/2 antiferromagnetic triangular-lattice Heisenberg model with the exchange constant J approximately 250 K. Regardless of the large magnetic interactions, the 1H NMR spectra show no indication of long-range magnetic ordering down to 32 mK, which is 4 orders of magnitude smaller than J. These results suggest that a quantum spin liquid state is realized in the close proximity of the superconducting state appearing under pressure.

This article is an introductory review of the physics of quantum spin liquid (QSL) states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semi-classical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semi-classical approaches fail once quantum mechanics become important and then describes the alternative approaches for addressing the problem. We discuss mainly spin 1/2 systems, and we spend most of our time in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called SU (2), U (1) or Z 2 spin liquid states. We review the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin (S > 1/2) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular lattice systems (κ-(ET) 2 Cu 2 (CN) 3 and EtMe 3 Sb[(Pd(dmit) 2 ] 2 ), kagome lattice systems (ZnCu 3 (OH) 6 Cl 2 ) and hyperkagome lattice systems (Na 4 Ir 3 O 8 ), is reviewed and compared against the corresponding theories.

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