Zero Curvature Condition for Quantum Criticality

• URL: http://arxiv.org/abs/2303.09591v2
• Date: Thu, 19 Jun 2025 02:36:29 GMT
• Title: Zero Curvature Condition for Quantum Criticality
• Authors: Chaoming Song,
• Abstract summary: We propose a geometric approach to quantum phase transitions (QPTs) that shifts focus from microscopic order to the competition between non-commuting operators.<n>We show that QPTs occur at zero-curvature points on the quantum observable space boundary, signaling maximal commutativity and suggesting an underlying integrable structure at criticality.
• Score: 0.4506616924250028
• License: http://creativecommons.org/licenses/by/4.0/
• 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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