We study the spin-gap phase in the one-dimensional t- J model, assuming that it is caused by the backward scattering process. Based on the renormalization group analysis and symmetry, we can determine the transition point between the Tomonaga-Luttinger liquid and the spin-gap phases, by the level crossing of the singlet and the triplet excitations. In contrast to the previous works, the obtained spin-gap region is unexpectedly large. We also determine that the universality class of the transition belongs to the k0ex0ex=0ex0ex1 SU(2) Wess-Zumino-Witten model.
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Nakamura et al. (1997) studied this question.
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