Spin-charge separation in a Binary Bose Gases in Optical Lattices

We derive the ground-state phase diagram of antiferromagnetic spin-1 bosons trapped in a square optical lattice in the limit of large negative quadratic Zeeman interaction, i.e., a limit where only two spin components $\sigma=\uparrow, \downarrow$ are involved. The system thus reduces to an interacting binary Bose gas. Our quantum Monte Carlo simulations reveal a phase transition from a $x-y$ ferromagnetic-order to a spin insulator without symmetry breaking, inside the Mott insulating phase with two particles per site. This 3D-XY transition is characterized by the establishment of a finite local magnetic moment along the $z$-axis and by counterflow superfluidity inside the Mott phase. When increasing the spin-spin interaction amplitude $U_2$, this transition merges with the Mott-superfluid transition and becomes first-order. We derive the phase diagram of the spin-charge separation with respect to $U_2$ parameter.