Exact solution for SU(2)-symmetry-breaking bosonic mixtures at strong interactions

We study the equilibrium properties of a one-dimensional mixture of two Tonks-Girardeau gases on a ring geometry in the limit of strongly repulsive interspecies interactions. We derive the exact many-body wave function and compare it to the SU(2) solution where intra- and interspecies interactions are also diverging but equal. We focus on the role of the SU(2) symmetry breaking on the behavior of the large- and short-distance correlations by studying the zero-momentum occupation number and the Tan's contact from the asymptotic behavior of the momentum distribution. Although the symmetry is only weakly broken, it has important consequences on spin correlations in the system as the reduction by a factor of two of the zero-momentum occupation number with respect to the SU(2) case in the thermodynamic limit and the decrease of the Tan's contact.

Automated summary

This study investigates the equilibrium properties of a one-dimensional mixture of two Tonks-Girardeau gases on a ring geometry under strongly repulsive interspecies interactions. The role of SU(2) symmetry breaking on the behavior of large- and short-distance correlations is studied, revealing important consequences for spin correlations in the system.