  The ground-state correlations are investigated for an isotropic transverse XY
chain which is constrained to carry either a current of magnetization J_M or a
current of energy J_E. We find that the effect of nonzero J_M on the
large-distance decay of correlations is twofold: i) oscillations are introduced
and ii) the amplitude of the power law decay increases with increasing current.
The effect of energy current is more complex. Generically, correlations in
current carrying states are found to decay faster than in the J_E=0 states,
contrary to expectations that correlations are increased by the presence of
currents. However, increasing the current, one reaches a special line where the
correlations become comparable to those of the J_E=0 states. On this line, the
symmetry of the ground state is enhanced and the transverse magnetization
vanishes. Further increase of the current destroys the extra symmetry but the
transverse magnetization remains at the high-symmetry, zero value.
