@misc{oai:repo.qst.go.jp:00066590,
 author = {Sakai, T. and Sakai, Toru},
 month = {Nov},
 note = {The S=1/2 kagome-lattice antiferromagnet is one of interesting frustrated quantum spin systems. The system is supposed to exhibit the quantum spin liquid in the ground state, which was proposed as a possible origin of the high-temprature superconductivity. The spin gap is an important physical quantity to characterize the spin liquid behavior. Whether the S=1/2 kagome-lattice antiferromagnet is gapless or has a finite spin gap, is still an 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[2,3]. On the other hand, some density matrix renormalization group (DMRG) calculations supported the gapped Z2 topological spin liquid theory[4,5]. Our recent numerical diagonalization analysis on the magnetization process of a distorted kagome-lattice antiferromagnet indicated that the perfect kagome-lattice system is just on a quantum critical point[6]. It would be a possible reason why it is difficult to determine whether the perfect kagome-lattice antiferromagnet is gapless or gapped. 
     In the present study, a field derivative analysis is applied for the spin gap issue of the kagome-lattice antiferromanget, using the numerical diagonalization data up to 42-spin clusters. It is consistent with our previous conclusion that it is gapless[7]. 

[1]H. Nakano and T. Sakai: J. Phys. Soc. Jpn. 80 (2011) 053704.
[2]Y. Ran, M. Hermele, P. A. Lee and X. -G. Wen: Phys. Rev. Lett. 98 (2007) 117205.
[3]Y. Iqbal, F. Becca, S. Sorella and D. Poilblanc: Phys. Rev. B 87 (2013) 060405(R).
[4]S. Yan, D. A. Huse and S. R. White: Science 332 (2011) 1173.
[5]S. Nishimoto, N. Shibata and C. Hotta: Nat. Commun. 4 (2013) 2287.
[6]H. Nakano and T. Sakai: J. Phys. Soc. Jpn. 83 (2014) 104710.
[7]H. Nakano and T. Sakai: in preparation., Symposium on Trends in Condensed Matter Physics},
 title = {Quantum Spin Liquid of Kagome-Lattice Antiferromagnet},
 year = {2017}
}