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.

在具有局部相互作用的量子多体系统中，至少对于足够大的系统，边界条件的影响被认为是可以忽略的。这里我们展示了一个相反的例子。我们考虑具有两个竞争相互作用的自旋链，该旋转链位于具有奇数个位点的环上。当仅主要的相互作用是反铁磁的，从而引起拓扑挫折时，标准的反铁磁阶（由磁化表示）被破坏。当第二种相互作用也从铁性转变为反铁性时，就会出现一个反铁磁顺序，其特征是依赖于位置的磁化强度在空间上以不相称的模式变化。这种调制来自基态简并性，它可以打破平移不变性。