In the Mott-insulator regime, two species of ultracold atoms in an optical lattice can exhibit the low-energy counterflow motion. We construct effective Hamiltonians for the three classes of the two-species (fermion-fermion, boson-boson, and boson-fermion-type) insulators and reveal the conditions when the resulting ground state supports super-counter-fluidity (SCF), with the alternative being phase segregation. We emphasize a crucial role of breaking the isotopic symmetry between the species for realizing the SCF phase.
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
σ=↑,↓ 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
U2, 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
U2 parameter.