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The $S=1/2$ quantum spin ladder system with the anisotropic ferromagneticexchange interaction on the rung under magnetic field is investigated using thenumerical diagonalization and the density matrix renormalization group (DMRG)analyses. It is found that the nematic-spin-correlation-dominantTomonaga-Luttinger liquid (TLL) appears in some high magnetic field. It isincluded in the TLL phase where the two-magnon bound state is realized. Forsome suitable parameters, after the field-induced phase transition from thistwo-magnon-bound TLL phase to the single-magnon TLL one, the re-entranttransition to the two-magnon-bound TLL phase occurs, which is confirmed by themagnetization curves by the DMRG. Several phase diagrams on the plane of thecoupling anisotropy versus the magnetization and the magnetic field arepresented. The present result is a proposal of the candidate system whichexhibits the spin nematic phase without the biquadratic interaction or thefrustration.

Field-induced spin nematic Tomonaga-Luttinger liquid of the $S=1/2$ spin ladder system with the anisotropic ferromagnetic rung interaction