Phase Diagram ofS=1/2 AntiferromagneticXXZChainwith Next-Nearest-Neighbor Interactions

We numerically investigate the critical lines of the fluid-dimer and the Néel-dimer transitions of the S =1/2 antiferromagnetic XXZ chain with next-nearest interactions, assuming the asymptotic behavior to be determined by the quantum sine-Gordon model. Our result is different from that of Tonegawa, Harada and Kaburagi, who used the phenomenological renormalization group (PRG). We show that the PRG may lead to a false critical point when it is applied to the Kosterlitz-Thouless-type transition.