Fractional vortices in a spin-isotropic spiral spin liquid
Abstract
Spiral spin liquids are magnetic states whose classical ground-state manifold consists of planar incommensurate spin spirals with wave vectors lying on a continuous ring or surface in reciprocal space. The resulting subextensive degeneracy suppresses magnetic long-range order and gives rise to liquid-like behavior. Despite numerous material realizations and theoretical investigations, the structure of low-temperature spin configurations of spin-isotropic Heisenberg spiral spin liquids has remained poorly understood. Here, we classify and characterize the classical topological defects supported by these systems. We uncover a rich family of vortex types involving concerted windings of spin directions, spiral-plane normals, and wave-vector orientations, yielding a ℤ × ℤ2 classification. Remarkably, the elementary defects are half-vortices carrying fractional 2π windings in both spin and momentum space and obey fusion rules resembling to those of Ising anyons. Large-scale classical simulations of a square-lattice spiral spin liquid reveal that these vortices are dense in the spiral-spin-liquid regime, and bind tightly below an order-by-disorder phase transition, eventually fusing to vacuum.
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BibTeX
@misc{glittum2026fractional,
title = {{Fractional vortices in a spin-isotropic spiral spin liquid}},
author = {Cecilie Glittum and Han Yan and Johannes Reuther},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15941},
eprint = {2609.15941},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15941},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fractional vortices in a spin-isotropic spiral spin liquid
AU - Cecilie Glittum
AU - Han Yan
AU - Johannes Reuther
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15941
UR - https://arxiv.org/abs/2609.15941
AB - Spiral spin liquids are magnetic states whose classical ground-state manifold consists of planar incommensurate spin spirals with wave vectors lying on a continuous ring or surface in reciprocal space. The resulting subextensive degeneracy suppresses magnetic long-range order and gives rise to liquid-like behavior. Despite numerous material realizations and theoretical investigations, the structure of low-temperature spin configurations of spin-isotropic Heisenberg spiral spin liquids has remained poorly understood. Here, we classify and characterize the classical topological defects supported by these systems. We uncover a rich family of vortex types involving concerted windings of spin directions, spiral-plane normals, and wave-vector orientations, yielding a ℤ × ℤ_2 classification. Remarkably, the elementary defects are half-vortices carrying fractional 2π windings in both spin and momentum space and obey fusion rules resembling to those of Ising anyons. Large-scale classical simulations of a square-lattice spiral spin liquid reveal that these vortices are dense in the spiral-spin-liquid regime, and bind tightly below an order-by-disorder phase transition, eventually fusing to vacuum.
ER -