Work

Quantum entanglement, stratified spaces, and topological matter: towards entanglement-sensitive Langlands data

Year: 2026

Type: article

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.

Source: Reports on Progress in Physics

DOI: 10.1088/1361-6633/ae73b6

Authors: Kazuki Ikeda, Steven Rayan

Institutions: University of Massachusetts Boston, Stony Brook University, University of Saskatchewan

Language: English

Topic: Topological Materials and Phenomena

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,680

Funders: National Science Foundation, Natural Sciences and Engineering Research Council of Canada