Phase diagram of spin-(1/2) bosons in a one-dimensional optical lattice

Systems of two coupled bosonic species are studied using mean field theory and the quantum Monte Carlo method. The phase diagram is characterized on the basis of both the mobility of the particles (Mott insulating or superfluid) and whether or not the system is magnetic (different populations for the two species). The phase diagram is shown to be population balanced for negative spin-dependent interactions, regardless of whether it is insulating or superfluid. For positive spin-dependent interactions, the superfluid phase is always polarized, and the two populations are imbalanced. However, the Mott-insulating phase with even commensurate filling always has balanced populations. In contrast, the Mott phase with odd commensurate filling has balanced populations in a very strong interaction and polarizes as the interaction gets weaker while still in the Mott phase.