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We have obtained an analytic expression for the $k$ dependence of excitationenergy gap for an arbitrary double $S=1/2$ spin-chain by using the nonlocalunitary transformation and the variational method. It is checked to explain thegap behavior of various systems, which include the Haldane system and the dimersystem in both extreme limits, and also the ladder model and the Majumdar-Ghoshmodel. The string order parameter, the dimer order parameter, and the localspin value are also calculated in the ground state. The ground-state energyexhibits a great stabilization by an antiferromagnetic bond dimerization, whichmight be realized in various new compounds. We also mention the relation of theconvergence to the Haldane state with the spin-exchange symmetry of the model.The excited state has one domain wall of a local triplet type except in thevicinity of the Majumdar-Ghosh point, where a local triplet is decomposed totwo $S=1/2$ free spins moving among the singlet dimers.Comment: 9 pages, REVTeX, 7 figures; Mistakes in the equation (11) and (13)  are correcte

Haldane and dimer gaps in general double-spin-chain models