  In one-dimensional systems a twisted superfluid phase is found which is
induced by a spontaneous breaking of the time-reversal symmetry. Using the
density-matrix renormalization group allows us to show that the excitation
energy gap closes exponentially causing a quasi-degenerate ground state. The
two degenerate ground states are connected by the time-reversal symmetry which
manifests itself in an alternating complex phase of the long-range correlation
function. The quantum phase transition to the twisted superfluid is driven by
pair tunneling processes in an extended Bose-Hubbard model. The phase
boundaries of several other phases are discussed including a supersolid, a pair
superfluid, and a pair supersolid phase as well as a highly unconventional Mott
insulator with a degenerate ground state and a staggered pair correlation
function.
