Gapless Quantum Spin Liquid of the Kagome-Lattice Antiferromagnet

The S=1/2 kagome-lattice antiferromagnet is one of interesting frustrated quantum spin systems. The spin gap is an important physical quantity to characterize the spin fluid behavior. Whether the S=1/2 kagome-lattice antiferromagnet is gapless or has a finite spin gap, is still unsolved issue. Because any recently developped numerical calculation methods are not enough to determine it in the thermodynamic limit. Our large-scale numerical diazonalization up to 42-spin clusters and a finite-size scaling analysis indicated that the S=1/2 kagome-lattice antiferromagnet is gapless in the thremodynamic limit[1]. It is consistent with the U(1) Dirac spin liquid theory of the kagome-lattice antiferromagnet. On the other hand, the density matrix renormalization group calculations supported the gapped Z2 topological spin liquid theory. We propose one of better methods to determine whether the spin excitation is gapless or gapped, based on the finite-size scaling analysis of the spin susceptibility calculated by the numerical diagonalization. The present work indicates that the kagome-lattice antiferromagnet is gapless[2].
[1]H. Nakano and T. Sakai, J. Phys. Soc. Jpn. 80, 053704 (2011), [2]H. Nakano and T. Sakai in preparation.