Few-Magnon Universality beyond Contact Interactions in Long-Range Spin Chains
Abstract
Quantum few-body systems exhibit a rich variety of phenomena that provide fundamental insights into universality. A paradigmatic example is the Efimov effect, in which an infinite tower of three-body bound states emerges with binding energies forming a geometric sequence. Motivated by advances in trapped-ion systems, recent theoretical work has predicted that the Efimov effect can arise in certain long-range quantum spin chains, where magnons exhibit a general dispersion εk=u|k|z with z∈(0.52,0.88) and interact through a contact potential. Nevertheless, whether Efimov universality persists in the presence of experimentally relevant long-range interactions between magnons remains unexplored. In this work, we address this issue by investigating the two- and three-magnon problems with a model interaction potential V(x)=V0/(1+|x|β). Our results demonstrate that few-body universality persists for any β>1: In the two-magnon sector, the low-energy expansion of the scattering matrix near a two-body resonance agrees with the universal form predicted by contact-interaction theory. The three-magnon bound-state spectrum exhibits Efimov scaling, with a scaling factor consistent with the theory. We further highlight the experimental relevance of our model, which can be readily realized in trapped-ion systems. Our results pave the way for quantum simulations of universal few-body physics beyond the traditional paradigm of nonrelativistic particles.
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BibTeX
@misc{huo2026fewmagnon,
title = {{Few-Magnon Universality beyond Contact Interactions in Long-Range Spin Chains}},
author = {Yiran Huo and Pengfei Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16126},
eprint = {2610.16126},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16126},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Few-Magnon Universality beyond Contact Interactions in Long-Range Spin Chains
AU - Yiran Huo
AU - Pengfei Zhang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16126
UR - https://arxiv.org/abs/2610.16126
AB - Quantum few-body systems exhibit a rich variety of phenomena that provide fundamental insights into universality. A paradigmatic example is the Efimov effect, in which an infinite tower of three-body bound states emerges with binding energies forming a geometric sequence. Motivated by advances in trapped-ion systems, recent theoretical work has predicted that the Efimov effect can arise in certain long-range quantum spin chains, where magnons exhibit a general dispersion ε_k=u|k|^z with z∈(0.52,0.88) and interact through a contact potential. Nevertheless, whether Efimov universality persists in the presence of experimentally relevant long-range interactions between magnons remains unexplored. In this work, we address this issue by investigating the two- and three-magnon problems with a model interaction potential V(x)=V_0/(1+|x|^β). Our results demonstrate that few-body universality persists for any β>1: In the two-magnon sector, the low-energy expansion of the scattering matrix near a two-body resonance agrees with the universal form predicted by contact-interaction theory. The three-magnon bound-state spectrum exhibits Efimov scaling, with a scaling factor consistent with the theory. We further highlight the experimental relevance of our model, which can be readily realized in trapped-ion systems. Our results pave the way for quantum simulations of universal few-body physics beyond the traditional paradigm of nonrelativistic particles.
ER -