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Recently it was highlighted that one-dimensional antiferromagnetic spin models with frustrated boundary conditions, i.e. periodic boundary conditions in a ring with an odd number of elements, may show very peculiar behavior. Indeed the presence of frustrated boundary conditions can destroy the magnetic order that characterizes such models when different boundary conditions are taken into account and induce novel phase transitions. Motivated by these results, we analyze the effects of the frustrated boundary conditions on several models supporting topological orders. In particular, we focus on the Cluster-Ising model, which presents a symmetry protected topologically ordered phase, and the Kitaev and AKLT chains that, on the contrary, are characterized by a purely topological order. In all these models we find that the different topological orders are not affected by the frustrated boundary conditions. This observation leads naturally to the conjecture that systems supporting topological order are resilient to topological frustration, and thus that topological phases could be identified through this resilience.
A central tenant in the classification of phases is that boundary conditions cannot affect the bulk properties of a system. In this work, we show striking, yet puzzling, evidence of a clear violation of this assumption. We use the prototypical exampl
It has been recently proven that new types of bulk, local order can ensue due to frustrated boundary condition, that is, periodic boundary conditions with an odd number of lattice sites and anti-ferromagnetic interactions. For the quantum XY chain in
Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this assumptio
At the core of every frustrated system, one can identify the existence of frustrated rings that are usually interpreted in terms of single--particle physics. We check this point of view through a careful analysis of the entanglement entropy of both m
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 in