Ground state properties of a multi-component bosonic mixture: a Gutzwiller mean-field study

Using the single-site Gutzwiller method, we theoretically study the ground state and the interspecies entanglement properties of interexchange symmetric multi-component (two- and three-) bosonic mixtures in an optical lattice, and the results are generalized to an $n$-component ($n=2,3,4,\cdots$) system. We compute the mean-field phase diagram, the interspecies entanglement entropy, and the ground state spectral decomposition. Three phases namely the $n$-component Superfluid state (nSF), the $n$-component Mott insulator state (nMI), and the Super-counter-fluid state (SCF) are observed. Interestingly, we find that there are $n-1$ SCF lobes to separate every two neighboring nMI lobes in the phase diagram. More importantly, we derive the exact general expression of the interspecies entanglement entropy for the SCF phase. In addition, we also investigate the demixing effect of an n-component mixture and demonstrate that the mixing-demixing critical point is independent of n.