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The spin gap of a one-dimensional repulsive Hubbard model is numericallycalculated with the density matrix renormalization group, with a specialemphasis on the effect of a next-nearest neighbor hopping (t') and thenearest-neighbor ferromagnetic exchange (J) interaction. At half-filling, asignificant spin gap opens if |t'| \simeq |t| and J=0, in agreement with theweak coupling theory, while the gap is strongly suppressed by the introductionof J. On the other hand, the quarter-filled system has very small spin gapsregardless of the values of t' and J. Implications for the CuO_2 chain inSr_{14}Cu_{24}O_{41} and related materials are discussed.

Density-matrix renormalization-group study of the spin gap in a one-dimensional Hubbard model: Effect of the distant transfer and exchange coupling