Fidelity and quantum phase transitions

Huan-Qiang Zhou; John Paul Barjaktarevic

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Fidelity and quantum phase transitions

Huan-Qiang Zhou·John Paul Barjaktarevic

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Abstract

It is shown that the fidelity, a basic notion of quantum information science, may be used to characterize quantum phase transitions, regardless of what type of internal order is present in quantum many-body states. If the fidelity of two given states vanishes, then there are two cases: (1) they are in the same phase if the distinguishability results from irrelevant local information; or (2) they are in different phases if the distinguishability results from relevant long-distance information. The different effects of irrelevant and relevant information are quantified, which allows us to identify unstable and stable fixed points (in the sense of renormalization group theory). A physical implication of our results is the occurrence of the orthogonality catastrophe near the transition points.

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Huan-Qiang Zhou, John Paul Barjaktarevic. 2007-01-25. Fidelity and quantum phase transitions. https://arxiv.org/abs/cond-mat/0701608

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