A mean field theory for the spin ladder system

In the present paper, we propose a mean field approach for spin ladders based upon the Jordan-Wigner transformation along an elaborately ordered path. We show on the mean field level that ladders with even number legs open a energy gap in their low energy excitation with a magnitude close to the corresponding experimental values, whereas the low energy excitation of the odd-number-leg ladders are gapless. It supports the validity of our approach. We then calculate the gap size and the excitation spectra of 2-leg-ladder system. Our result is in good agreement with both the experimental data and the numerical results.