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We study the ground state of frustrated spin-S chains in a strong magneticfield in the immediate vicinity of saturation. In strongly frustrated chains,the magnon dispersion has two degenerate minima at inequivalent momenta $\pmQ$, and just below the saturation field the system can be effectivelyrepresented as a dilute one-dimensional lattice gas of two species of bosonsthat correspond to magnons with momenta around $\pm Q$. We present a theory ofeffective interactions in such a dilute magnon gas that allows us to makequantitative predictions for arbitrary values of the spin. With the help ofthis method, we are able to establish the magnetic phase diagram of frustratedchains close to saturation and study phase transitions between severalnontrivial states, including a two-component Luttinger liquid, a vector chiralphase, and phases with bound magnons. We study those phase transitionsnumerically and find a good agreement with our analytical predictions.

Frustrated spin chains in strong magnetic field: dilute two-component Bose gas regime