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 similar to 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.