Topologically Frustrated Spin Chains

In quantum many-body systems with local interactions, the effects of boundary conditions are considered to be negligible, at least for sufficiently large systems. We show examples of the opposite by considering spin-1/2 chains which contain antiferromagnetic interactions and are set on a ring with an odd number of sites – a setting inducing topological frustration. In particular, we focus on different spin chains which possess a global SU(2) symmetry with parity symmetries,  a quite general condition in the absence of external fields. This condition implies, even at finite sizes, an exact degeneracy of the ground state, and enables computing the magnetization already in a finite system, so that we can follow it towards the thermodynamic limit. We find in this way that topological frustration can destroy local order, create a site-dependent magnetization which varies in space with an incommensurate pattern, induce a new quantum phase transition and modify the existing one, by destroying local order parameters on both sides of the transition so that the two thermodynamic phases can only be characterized by string order parameters.