Exact admissibility radii for the lattice topological charge of quantum spin textures
Abstract
How much can a magnetic field change before a quantum spin texture loses its skyrmion charge? For a triangulated spin-s texture on N quantum sites, we determine the smallest change in its local moments that makes the reconstructed topological charge ill-defined, allowing unequal error bounds and fixed boundary moments. Combined with spectral perturbation theory, this geometric threshold yields explicit magnetic-field intervals that preserve the ground-state charge, scaling as 1/N when the gap and geometric margin have positive limits. We apply the bounds to finite spin-1/2 systems with exchange and Dzyaloshinskii-Moriya interactions. In a rigorously verified seven-spin example the charge changes at a single certified field, while the excitation gap and all local spin polarizations remain bounded away from zero; there the geometric margin vanishes linearly.
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BibTeX
@misc{galan2026exact,
title = {{Exact admissibility radii for the lattice topological charge of quantum spin textures}},
author = {Raúl Sánchez Galán and Robert Wieser},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14172},
eprint = {2609.14172},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14172},
}
RIS
TY - UNPB
TI - Exact admissibility radii for the lattice topological charge of quantum spin textures
AU - Raúl Sánchez Galán
AU - Robert Wieser
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.14172
UR - https://arxiv.org/abs/2609.14172
AB - How much can a magnetic field change before a quantum spin texture loses its skyrmion charge? For a triangulated spin-s texture on N quantum sites, we determine the smallest change in its local moments that makes the reconstructed topological charge ill-defined, allowing unequal error bounds and fixed boundary moments. Combined with spectral perturbation theory, this geometric threshold yields explicit magnetic-field intervals that preserve the ground-state charge, scaling as 1/N when the gap and geometric margin have positive limits. We apply the bounds to finite spin-1/2 systems with exchange and Dzyaloshinskii-Moriya interactions. In a rigorously verified seven-spin example the charge changes at a single certified field, while the excitation gap and all local spin polarizations remain bounded away from zero; there the geometric margin vanishes linearly.
ER -