We consider two species of bosons in one dimension near the Tonks-Girardeau limit of infinite interactions. For the case of equal masses and equal intraspecies interactions, the system can be mapped to a $S=1/2$ $XXZ$ Heisenberg spin chain, thus allowing one to access different magnetic phases. Using a powerful ansatz developed for the two-component Fermi system, we elucidate the evolution from few to many particles for the experimentally relevant case of an external harmonic confinement. In the few-body limit, we already find clear evidence of both ferromagnetic and antiferromagnetic spin correlations as the ratio of intraspecies and interspecies interactions is varied. Furthermore, we observe the rapid emergence of symmetry-broken magnetic ground states as the particle number is increased. We therefore demonstrate that systems containing only a few bosons are an ideal setting in which to realize the highly sought-after itinerant ferromagnetic phase.

• Received 22 July 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.247202