Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data

Abstract:Using the spinless Haldane model, we study the witness-filtered Berry curvature, quantum geometric tensor, and quantum Fisher information on the gapped strata of the parameter space and evaluate them through the Fukui-Hatsugai-Suzuki discretization. The filtered quantities isolate the part of the geometric response carried by sublattice coherence: they suppress contributions from regions where the occupied Bloch state is locally A/B-separable and emphasize regions where curvature and coherence coexist. We derive exact lattice identities, reconstruction formulas for the curvature-weighted coherence, and bounds relating the filtered quantum geometric tensor and quantum Fisher information to single-particle mode entanglement. Across the gap-closing stratum, the quantized response changes admit a natural description in terms of Hecke modifications. We elicit a corresponding Langlands viewpoint -- not as a full correspondence, but as an organizational principle and as the mathematical shadow of these physical geometric constructions.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph); Representation Theory (math.RT)

arXiv:2601.13467 [quant-ph]

(or arXiv:2601.13467v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2601.13467 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1088/1361-6633/ae73b6 Focus to learn more DOI(s) linking to related resources

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