  To clarify the transport property mediated by bound magnons in a spin nematic
state, we investigate the spin Drude weight of a spin-1/2 $J_{1}$-$J_{2}$
Heisenberg chain with ferromagnetic $J_{1}$ and antiferromagnetic $J_{2}$ in a
magnetic field by numerical diagonalization. At zero magnetic field, numerical
results with up to 24 sites suggest that the spin Drude weight would be zero in
the thermodynamic limit, indicating diffusive spin transport. With increasing
the magnetic field, the spin Drude weight is enhanced at low temperatures,
indicating that bound magnons would contribute to the spin transport.
