  In quantum many-body systems with local interactions, the effects of boundary
conditions are considered to be negligible, at least for sufficiently large
systems. Here we show an example of the opposite. We consider a spin chain with
two competing interactions, set on a ring with an odd number of sites. When
only the dominant interaction is antiferromagnetic, and thus induces
topological frustration, the standard antiferromagnetic order (expressed by the
magnetization) is destroyed. When also the second interaction turns from ferro
to antiferro, an antiferromagnetic order characterized by a site-dependent
magnetization which varies in space with an incommensurate pattern, emerges.
This modulation results from a ground state degeneracy, which allows to break
the translational invariance. The transition between the two cases is signaled
by a discontinuity in the first derivative of the ground state energy and
represents a quantum phase transition induced by a special choice of boundary
conditions.
