What Becomes of the Antiferromagnetic String When Long Range Neel Order Is Lost? Exact Results
Abstract
Early string descriptions of doped antiferromagnets associate hole motion in a locally Néel-ordered background with a path-dependent antiferromagnetic string. We ask what becomes of this mechanism when long range Néel order is lost while short range antiferromagnetic correlations persist. In a singlet bond representation, the underlying basis states do not assign an oriented A/B spin registration to each bond. Therefore, any surviving long wavelength antiferromagnetic axis is naturally described as a director, n∼−n. Long range Néel order can nevertheless provide a global S2 lift of this director field; when that long range registration is lost, non liftable configurations of the RP2 manifold become physically accessible, opening a topologically nontrivial ℤ2 sector. Its elementary defects are half vortices that globally minimize the RP2 σ-model energy within the nontrivial ℤ2 sector. An \textit{a posteriori} energetic comparison further shows that the projective half vortex texture is softer than the corresponding vector reference texture. A pair of half vortices with opposite windings is logarithmically confined, V(R) = κln(R/rcore), κ= πρs /2. The resulting confinement is carried not by a one dimensional string but by an extended two-dimensional spin texture. Thus, the loss of long-range Néel order does not eliminate antiferromagnetic confinement but removes the global Néel lift. This activates a distinct projective mechanism in which a local path dependent string is replaced, at long wavelengths, by a global topological texture with logarithmic confinement.
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BibTeX
@misc{dimaggio2026what,
title = {{What Becomes of the Antiferromagnetic String When Long Range Neel Order Is Lost? Exact Results}},
author = {Yuri DiMaggio},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.30346},
eprint = {2609.30346},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30346},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - What Becomes of the Antiferromagnetic String When Long Range Neel Order Is Lost? Exact Results
AU - Yuri DiMaggio
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2609.30346
UR - https://arxiv.org/abs/2609.30346
AB - Early string descriptions of doped antiferromagnets associate hole motion in a locally Néel-ordered background with a path-dependent antiferromagnetic string. We ask what becomes of this mechanism when long range Néel order is lost while short range antiferromagnetic correlations persist. In a singlet bond representation, the underlying basis states do not assign an oriented A/B spin registration to each bond. Therefore, any surviving long wavelength antiferromagnetic axis is naturally described as a director, n∼−n. Long range Néel order can nevertheless provide a global S^2 lift of this director field; when that long range registration is lost, non liftable configurations of the RP^2 manifold become physically accessible, opening a topologically nontrivial ℤ_2 sector. Its elementary defects are half vortices that globally minimize the RP^2 σ-model energy within the nontrivial ℤ_2 sector. An \textit{a posteriori} energetic comparison further shows that the projective half vortex texture is softer than the corresponding vector reference texture. A pair of half vortices with opposite windings is logarithmically confined, V(R) = κln(R/r_core), κ= πρ_s /2. The resulting confinement is carried not by a one dimensional string but by an extended two-dimensional spin texture. Thus, the loss of long-range Néel order does not eliminate antiferromagnetic confinement but removes the global Néel lift. This activates a distinct projective mechanism in which a local path dependent string is replaced, at long wavelengths, by a global topological texture with logarithmic confinement.
ER -