We demonstrate the existence of a form of topological order in the Luttinger liquid state, which appears crucial to the notion of spin-charge separation.This order, which is closely related to the hidden order characterizing the Haldane spin chains, appears to be incompletely specified in the Tomonaga-Luttinger picture from bosonization.Thus, we use numerical calculations to complete the picture.
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Kruis et al. (2004) studied this question.
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