Field-Induced Spin Nematic Phase in the $S=1$ Anisotropic Spin Ladder

The S=1 spin ladder with the easy-axis single-ion anisotropy is investigated using the numerical diagonalization and the finite-size scaling analysis. It is found that the field-induced nematic Tomonaga-Luttinger liquid phase appears above the critical field. In addition, there exists another critical field at which the quantum phase transition from the nematic Tomonaga-Luttinger liquid phase to the conventional field-induced Tomonaga- Luttinger liquid phase occurs. Besides some phase diagrams are presented.