Theory of spin gaps in the dimerized quarter-filled two-leg rectangular ladder

Despite the extensive work on even-leg spin-ladders and 1/2- filled band electron-ladders \footnote{E. Dagotto and T.M. Rice, Science {\bf 271}, 618 (1996).} , little is known currently about commensurate non-1/2-filled band electron ladders. We report density-matrix renormalization group calculations of spin gaps in the 1/4-filled band correlated two-leg rectangular ladder with dimerization along the legs of the ladder. In contrast to the uniform ladder, spin gaps in the dimerized ladder can be significant. Very large spin gaps, as are found experimentally in quarter-filled band organic charge-transfer solids with coupled pairs of quasi-one-dimensional stacks \footnote{E. Ribera et al., Chem. Eur. J. 5, 2025 (1999).}, however, occur within the model only for large leg dimerization and electron hopping along the rungs that are nearly equal to the hopping along the legs.