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arXiv · 2303.09591

Zero Curvature Condition for Quantum Criticality

Chaoming Song
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Abstract

Quantum criticality often lies beyond the scope of the conventional Landau paradigm, and a unifying framework has yet to emerge, due in part to the wide variety of quantum orders. We propose a geometric approach to quantum phase transitions (QPTs) that shifts focus from microscopic order to the competition between non-commuting operators. This competition is encoded in the boundary geometry of their expectation values, defining a quantum observable space (QOS). We show that QPTs occur at zero-curvature points on the QOS boundary, signaling maximal commutativity and suggesting an underlying integrable structure at criticality.

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Chaoming Song. 2023-03-16. Zero Curvature Condition for Quantum Criticality. https://doi.org/10.1103/l3d5-lnr7

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