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

TL;DR

This paper derives an exact solution for a strongly-interacting two-component bosonic mixture in one dimension, analyzing how weak $SU(2)$ symmetry breaking affects correlations, momentum distribution, and Tan's contact.

Contribution

It provides an exact many-body wavefunction for the system and investigates the effects of $SU(2)$-symmetry breaking on correlation functions and momentum properties.

Findings

Weak symmetry breaking reduces zero-momentum occupation by half in the thermodynamic limit.

Tan's contact decreases due to symmetry breaking.

Correlation functions are significantly affected by the symmetry breaking.

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.