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Fragility of String Orders

F. Anfuso·A. Rosch
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Abstract

One-dimensional gapped systems are often characterized by a 'hidden' non-local order parameter, the so-called string order. Due to the gap, thermodynamic properties are robust against a weak higher-dimensional coupling between such chains or ladders. To the contrary, we find that the string order is not stable and decays for arbitrary weak inter-chain or inter-ladder coupling. We investigate the vanishing of the order for three different systems: spin-one Haldane chains, band insulators, and the transverse-field Ising model. Using perturbation theory and bosonization, we show that the fragility of the string order arises from non-local commutation relations between the non-local order parameter and the perturbation.

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F. Anfuso, A. Rosch. 2007-09-04. Fragility of String Orders. https://doi.org/10.1103/physrevb.76.085124

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