Incollection,

Fragility of String Orders

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Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)

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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