Dynamics of a one-dimensional spinor Bose liquid: A phenomenological approach

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 wave number q with the period of 2πn, 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, ω→ ωm (q,n). Without using any specific model of the interparticle interactions, we relate the corresponding exponents to independently measurable quantities ∂ ωm /∂q and ∂ ωm /∂n.