Evaluating Chern Topology in Discretized Brillouin Zones Using Bargmann Invariants
Abstract
We develop a finite-state geometric framework based on third-order Bargmann invariants for evaluating Chern numbers and characterizing local quantum-state geometry. Using gauge-invariant state overlaps, the framework evaluates the Chern number directly on discretized parameter spaces while retaining local geometric information through the phase-derived density and the complementary amplitude density, as well as signatures associated with changes in topological character. We apply the construction to the Qi--Wu--Zhang, 1/3- and 1/4-flux Hofstadter, SSH, and Rice--Mele models, including a rank-$2$ extension for isolated composite subspaces and applications to closed-loop and parameter-space topology. The resulting framework organizes Chern topology and local geometric information directly from finite-state data, providing a compact state-based description without relying on dynamical evolution.
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BibTeX
@misc{sangiri2026evaluating,
title = {{Evaluating Chern Topology in Discretized Brillouin Zones Using Bargmann Invariants}},
author = {Swarup Sangiri and A Taraphder},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03104},
eprint = {2610.03104},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03104},
}
RIS
TY - UNPB
TI - Evaluating Chern Topology in Discretized Brillouin Zones Using Bargmann Invariants
AU - Swarup Sangiri
AU - A Taraphder
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03104
UR - https://arxiv.org/abs/2610.03104
AB - We develop a finite-state geometric framework based on third-order Bargmann invariants for evaluating Chern numbers and characterizing local quantum-state geometry. Using gauge-invariant state overlaps, the framework evaluates the Chern number directly on discretized parameter spaces while retaining local geometric information through the phase-derived density and the complementary amplitude density, as well as signatures associated with changes in topological character. We apply the construction to the Qi--Wu--Zhang, 1/3- and 1/4-flux Hofstadter, SSH, and Rice--Mele models, including a rank-$2$ extension for isolated composite subspaces and applications to closed-loop and parameter-space topology. The resulting framework organizes Chern topology and local geometric information directly from finite-state data, providing a compact state-based description without relying on dynamical evolution.
ER -