Successive magnetic-phase transitions in a frustrated two-leg spin ladder

Recently, successive phase transitions induced by magnetic field have been observed in a frustrated two-leg spin ladder BiCu$_2$PO$_6$, in which the frustration is introduced by the next-nearest-neighbor antiferromagnetic exchange interaction in the leg direction. First, we calculate the magnetic-field dependence of magnetization by using density-matrix renormalization-group method. In this calculation, we find a phase transition induced by strong frustration, which does not appear in a non-frustrated two-leg spin ladder. The phase transition emerges as a jump of susceptibility with unsaturated finite magnetization. We also investigate the origin of the phase transition by using the bond-operator mean-field approximation. We conclude that the phase transition is the same type as the Lifshitz transition. Our study is useful to analyze experimental data of BiCu$_2$PO$_6$.