Dimer-dimer zero crossing and dilute dimerized liquid in a one-dimensional mixture

We consider the system of dimers formed in a one-dimensional mass-balanced Bose-Bose mixture of species $\sigma =\uparrow$, $\downarrow$ with attractive interspecies and repulsive intraspecies contact interactions. In the plane parametrized by the ratios of the coupling constants $g_{\uparrow \uparrow }\mathrm{/}\mathrm{\mid }{g}_{\uparrow \downarrow }\mathrm{\mid }$ and $g_{\downarrow \downarrow }\mathrm{/}\mathrm{\mid }{g}_{\uparrow \downarrow }\mathrm{\mid }$ we trace out the curve where the dimer-dimer interaction switches from attractive to repulsive. We find this curve to be significantly (by more than a factor of 2) shifted towards larger $g_{\sigma \sigma }$ (or smaller $\mathrm{\mid }{g}_{\uparrow \downarrow }\mathrm{\mid }$) compared to the mean-field stability boundary $g_{\uparrow \uparrow }{g}_{\downarrow \downarrow }=g_{\uparrow \downarrow }^2$. For a weak dimer-dimer attraction we predict a dilute dimerized liquid phase stabilized against collapse by a repulsive three-dimer force.