The ground state of a spinor Bose liquid is ferromagnetic, while the softest excitation above the ground state is the magnon mode. The dispersion relation of the magnon in a one-dimensional liquid is periodic in the wavenumber q with the period 2pi n
, determined by the density n of the liquid. Dynamic correlation functions, such as e.g. spin-spin correlation function, exhibit power-law singularities at the magnon spectrum, $omegatoomega_m(q,n)$. Without using any specific model of the inter-particle interactions, we relate the corresponding exponents to independently measurable quantities $partialomega_m/partial q$ and $partialomega_m/partial n$.
We show that the dynamic structure factor of a one-dimensional Bose liquid has a power-law singularity defining the main mode of collective excitations. Using the Lieb-Liniger model, we evaluate the corresponding exponent as a function of the wave vector and the interaction strength.
