Polarization suppression and nonmonotonic local two-body correlations in the two-component Bose gas in one dimension

We study the interplay of quantum statistics, strong interactions, and finite temperatures in the two-component (spinor) Bose gas with repulsive delta-function interactions in one dimension. Using the Thermodynamic Bethe Ansatz, we obtain the equation of state, population densities, and local density correlation numerically as a function of all physical parameters (interaction, temperature, and chemical potentials), quantifying the full crossover between low-temperature ferromagnetic and high-temperature unpolarized regimes. In contrast to the single component, Lieb-Liniger gas, nonmonotonic behavior of the local density correlation as a function of temperature is observed.