Zero Curvature Condition for Quantum Criticality
Quantum Physics
2025-06-23 v2
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.
Cite
@article{arxiv.2303.09591,
title = {Zero Curvature Condition for Quantum Criticality},
author = {Chaoming Song},
journal= {arXiv preprint arXiv:2303.09591},
year = {2025}
}