Spectral Crossings Diagnose Multiply Quantized Vortex Splitting
Abstract
A charge-r coupling vortex can remain as one fused order-r zero or split into r nearby unit-charge zeros after weak symmetry breaking. The two configurations have the same total winding and the same number of dark states in the lowest-Landau-level projection, so neither the imposed orbital angular momentum nor the total winding number distinguishes their local geometry. We study this distinction in a two-component Haldane-sphere model coupled by a Raman field. For monopole flux N, the detuning τc at which a defect branch crosses zero energy scales as |τc|∼ N−(r+1) for a fused zero and N−2 for resolved unit zeros. A Feshbach reduction establishes these asymptotic laws for the full multiband Hamiltonian, and numerical calculations in a monopole-harmonic basis confirm the fused-vortex scaling for r=1,2,3. For a partially split cluster of diameter d, the scaling crosses over when d is comparable to the magnetic length ℓB, allowing d to be inferred spectroscopically even below the spatial resolution of direct imaging.
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BibTeX
@misc{baek2026spectral,
title = {{Spectral Crossings Diagnose Multiply Quantized Vortex Splitting}},
author = {Jongheon Baek and Hiroyuki Tajima and Gihwan Nam},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02234},
eprint = {2610.02234},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02234},
}
RIS
TY - UNPB
TI - Spectral Crossings Diagnose Multiply Quantized Vortex Splitting
AU - Jongheon Baek
AU - Hiroyuki Tajima
AU - Gihwan Nam
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02234
UR - https://arxiv.org/abs/2610.02234
AB - A charge-r coupling vortex can remain as one fused order-r zero or split into r nearby unit-charge zeros after weak symmetry breaking. The two configurations have the same total winding and the same number of dark states in the lowest-Landau-level projection, so neither the imposed orbital angular momentum nor the total winding number distinguishes their local geometry. We study this distinction in a two-component Haldane-sphere model coupled by a Raman field. For monopole flux N, the detuning τ_c at which a defect branch crosses zero energy scales as |τ_c|∼ N^−(r+1) for a fused zero and N^−2 for resolved unit zeros. A Feshbach reduction establishes these asymptotic laws for the full multiband Hamiltonian, and numerical calculations in a monopole-harmonic basis confirm the fused-vortex scaling for r=1,2,3. For a partially split cluster of diameter d, the scaling crosses over when d is comparable to the magnetic length ℓ_B, allowing d to be inferred spectroscopically even below the spatial resolution of direct imaging.
ER -