Density Matrix Renormalization Group Study of the Spin 1/2 Heisenberg Ladder with Antiferromagnetic Legs and Ferromagnetic Rungs

The ground state and low lying excitation of the spin 1/2 Heisenberg ladder with antiferromagnetic leg ($J$) and ferromagnetic rung ($-\lambda J, \lambda >0$) interaction is studied by means of the density matrix renormalization group method. It is found that the state remains in the Haldane phase even for small $\lambda \sim 0.02$ suggesting the continuous transition to the gapless phase at $\lambda = 0$. The critical behavior for small $\lambda$ is studied by the finite size scaling analysis. The result is consistent with the recent field theoretical prediction.