  Strongly interacting systems have been conjectured to spontaneously develop
current carrying ground states under certain conditions. We conclusively
demonstrate the existence of a commensurate staggered interlayer current phase
in a bi-layer model by using the recently discovered quantum Monte-Carlo
algorithm without the sign problem. A pseudospin SU(2) algebra and the
corresponding anisotropic spin-1 Heisenberg model are constructed to show the
competition among the staggered interlayer current, rung singlet and charge
density wave phases.
