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تسجيل مستخدم جديدThe Frustration of being Odd: How Boundary Conditions can destroy Local Order
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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 example of an XYZ chain with no external field in a ring geometry with an odd number of sites and both ferromagnetic and antiferromagnetic interactions. In such a setting, even at finite sizes, we are able to calculate directly the spontaneous magnetizations that are traditionally used as order parameters to characterize the systems phases. When ferromagnetic interactions dominate, we recover magnetizations that in the thermodynamic limit lose any knowledge about the boundary conditions and are in complete agreement with standard expectations. On the contrary, when the system is governed by antiferromagnetic interactions, the magnetizations decay algebraically to zero with the system size and are not staggered, despite the AFM coupling. We term this behavior {it ferromagnetic mesoscopic magnetization}. Hence, in the antiferromagnetic regime, our results show an unexpected dependence of a local, one--spin expectation values on the boundary conditions, which is in contrast with predictions from the general theory.
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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 fr
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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
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