Fidelity and quantum phase transitions

TL;DR

This paper demonstrates that quantum fidelity can effectively characterize quantum phase transitions by distinguishing relevant from irrelevant information, revealing stable and unstable fixed points and the orthogonality catastrophe near critical points.

Contribution

It introduces a fidelity-based framework to identify quantum phase transitions and differentiate phases based on information relevance, linking to renormalization group concepts.

Findings

Fidelity vanishing indicates phase transition or same phase depending on information relevance.

Quantification of irrelevant and relevant information distinguishes stable and unstable fixed points.

Near transition points, the orthogonality catastrophe occurs, affecting state distinguishability.

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.