Quantum correlations and spatial localization in trapped one-dimensional ultra-cold Bose-Bose-Bose mixtures

We systematically investigate and illustrate the complete ground-state phase diagram for a one-dimensional, three-species mixture of a few repulsively interacting bosons trapped harmonically. To numerically obtain the solutions to the many-body Schrödinger equation, we employ the improved Exact Diagonalization method [T. D. Anh-Tai {\it et al.}, SciPost Physics 15, 048 (2023)], which is capable of treating strongly-correlated few-body systems from first principles in an efficiently truncated Hilbert space. We present our comprehensive results for all possible combinations of intra- and interspecies interactions in the extreme limits that are either the ideal limit ($g=0$) or close to the hard-core limit ($g\to \mathrm{\infty }$). These results show the emergence of unique ground-state properties related to correlations, coherence and spatial localization stemming from strongly repulsive interactions.