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

Abstract

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 inter-species interactions. We derive the exact many-body wavefunction and compare it to the $SU(2)$ solution where intra- and inter-species interactions are also diverging but equal. We focus on the role of the $SU(2)$-symmetry breaking on the behaviour 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.

9 pages, 5 figures

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• High-momentum oscillating tails of strongly interacting 1D gases in a box
• Symmetry oscillations in strongly interacting one-dimensional mixtures
• Quantum correlations and spatial localization in trapped one-dimensional ultra-cold Bose-Bose-Bose mixtures
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Asymmetric Bethe Ansatz
• Dynamical probing of high-order spin coherence in one-dimensional mixtures
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Shortcut to spin dynamics for quantum mixtures
• Space-time first-order correlations of an open Bose-Hubbard model with incoherent pump and loss
• Necklace Ansatz for strongly repulsive spin mixtures on a ring
• Symmetry oscillations sensitivity to SU(2)-symmetry breaking in quantum mixtures