Phase diagram of the spin-1/2 bond-alternating two-leg ladder

We study phase transition between two topologically different gapped states in the spin-1/2 bond-alternating two-leg Heisenberg ladder by investigating string order parameters and the level-crossing method based on the exact diagonalization. We determine the phase diagram on the plane of the bond-alternation delta and the rung-leg coupling ratio J(perpendicular to)/J, and conclude that the boundary is given as J(perpendicular to)/J proportional to delta(2/3) in the weak coupling region J(perpendicular to)/J, delta much less than 1.