Modular chaos, operator algebras, and the Berry phase
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13130_2025_Article_27166.pdf
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Author(s)
de Boer, Jan
Najian, Bahman
van der Heijden, Jeremy
Zukowski, Claire
Date Issued
September 10, 2025
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
de Boer, J., Najian, B., van der Heijden, J. et al. Modular chaos, operator algebras, and the Berry phase. J. High Energ. Phys. 2025, 86 (2025).
Version
Final published version
Abstract
Modular Berry transport associates a geometric phase to a zero mode ambiguity in a family of modular operators. In holographic settings, this phase was shown to encode nontrivial information about the emergent spacetime geometry. We reformulate modular Berry transport for arbitrary von Neumann algebras, including giving a precise definition of the zero mode projection in terms of a conditional expectation. For a certain class of state perturbations, we demonstrate that the modular Berry phase gives rise to an emergent symplectic form in the large N limit, extending related results in the context of subregion/subalgebra duality. We also show that the vanishing of the Berry curvature for modular scrambling modes signals the emergence of a local Poincaré algebra, which plays a key role in the quantum ergodic hierarchy. These results provide an intriguing relation between geometric phases, modular chaos and the local structure of spacetime.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/JHEP09(2025)086
