Weyl Chirality and Kitaev Topology through Bargmann Invariants
Abstract
We apply a finite-state geometric formulation based on Bargmann invariants to a two-band Weyl Hamiltonian and the one-dimensional Kitaev model of a p-wave superconductor. For the Weyl system, a symmetry-antisymmetrized third-order Bargmann combination selects the chirality-sensitive component of the local pseudospin geometry and extends to a two-band lattice Weyl model. For the Kitaev chain, a normalized ratio involving a third-order Bargmann invariant and a second-order overlap factor removes the dependence on an intermediate state and reproduces the Z2 distinction between its two gapped phases. We further construct a fourth-order loop connecting localized Majorana edge-mode profiles with finite-energy BdG states and an alternating fourth-order loop involving opposite Weyl pseudospin sectors. These constructions illustrate how suitable Bargmann combinations can probe chirality-sensitive, topological, and higher-order geometric information directly through quantum-state overlaps, providing an alternative state-based route without requiring a continuous description of the underlying state-space geometry.
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BibTeX
@misc{sangiri2026weyl,
title = {{Weyl Chirality and Kitaev Topology through Bargmann Invariants}},
author = {Swarup Sangiri and A. Taraphder},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25278},
eprint = {2609.25278},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25278},
}
RIS
TY - UNPB
TI - Weyl Chirality and Kitaev Topology through Bargmann Invariants
AU - Swarup Sangiri
AU - A. Taraphder
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25278
UR - https://arxiv.org/abs/2609.25278
AB - We apply a finite-state geometric formulation based on Bargmann invariants to a two-band Weyl Hamiltonian and the one-dimensional Kitaev model of a p-wave superconductor. For the Weyl system, a symmetry-antisymmetrized third-order Bargmann combination selects the chirality-sensitive component of the local pseudospin geometry and extends to a two-band lattice Weyl model. For the Kitaev chain, a normalized ratio involving a third-order Bargmann invariant and a second-order overlap factor removes the dependence on an intermediate state and reproduces the Z_2 distinction between its two gapped phases. We further construct a fourth-order loop connecting localized Majorana edge-mode profiles with finite-energy BdG states and an alternating fourth-order loop involving opposite Weyl pseudospin sectors. These constructions illustrate how suitable Bargmann combinations can probe chirality-sensitive, topological, and higher-order geometric information directly through quantum-state overlaps, providing an alternative state-based route without requiring a continuous description of the underlying state-space geometry.
ER -