The Frustration of being Odd: How Boundary Conditions can destroy Local Order

Vanja Marić, Salvatore Marco Giampaolo, Domagoj Kuić, Fabio Franchini

Published 2019-08-28Version 1

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 interaction. In such setting, we can calculate directly the magnetizations that are traditionally used as order parameters to characterize the phases of the system. When the ferromagnetic interaction dominates, we recover magnetizations that in the thermodynamic limit lose any knowledge about the boundary conditions and are in complete agreement with the standard expectations. On the contrary, when the system is governed by the anti-ferromagnetic interaction, the magnetizations decay algebraically to zero with the system size and it is not staggered, despite the AFM coupling. We term this behavior ferromagnetic mesoscopic magnetization. Hence, in the antiferromagnetic regime, our results show an unexpected dependence of a local, one-point function on the boundary conditions, that is in contrast with the predictions of the general theory.