Abstract
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.
Highlights
In quantum many-body systems with local interactions, the effects of boundary conditions are considered to be negligible, at least for sufficiently large systems
In14 a concrete example of a boundary-driven quantum phase transition was provided, showing that, by tuning the coupling between the edges of an open chain, the system can visit different phases. In this line of research, particular attention was devoted to analyzing onedimensional translational-invariant antiferromagnetic (AFM) spin models with frustrated boundary conditions (FBC), i.e, periodic boundary conditions in rings with an odd number of sites N
We illustrate our results by discussing the XY chain at zero field in FBC
Summary
In quantum many-body systems with local interactions, the effects of boundary conditions are considered to be negligible, at least for sufficiently large systems. Topologically ordered phases[5,6], which have no equivalent in the classical regime, as well as nematic ones[7], represent instances in which violation of the same symmetry is associated with different (typically non-local) and non-equivalent order parameters[8,9,10], depending on the model under analysis This implied that Landau’s theory had to be extended to incorporate more general concepts of order, which include the non-local effects that come along with the quantum regime and have no classical counterpart. In[14] a concrete example of a boundary-driven quantum phase transition was provided, showing that, by tuning the coupling between the edges of an open chain, the system can visit different phases In this line of research, particular attention was devoted to analyzing onedimensional translational-invariant antiferromagnetic (AFM) spin models with frustrated boundary conditions (FBC), i.e, periodic boundary conditions in rings with an odd number of sites N. The vanishing of the spontaneous magnetization and the replacement of the standard AFM local order with a mesoscopic ferromagnetic one was established through the direct evaluation of the one-point function in refs. 20,21
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