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arXiv:2610.16126

Few-Magnon Universality beyond Contact Interactions in Long-Range Spin Chains

Yiran Huo, Pengfei Zhang

cond-mat.quant-gasquant-phSubmitted Oct 12, 2026• Announced Oct 13, 2026• 0 citations
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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 $ε_k=u|k|^z$ with $z\in(0.52,0.88)$ 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.

Comments
10 pages, 4 figures

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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∣zε_k=u|k|^zεk​=u∣k∣z with z∈(0.52,0.88)z\in(0.52,0.88)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)V(x)=V_0/(1+|x|^β)V(x)=V0​/(1+∣x∣β). Our results demonstrate that few-body universality persists for any β>1β>1β>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.
Understanding how quasi-particles interact with impurities is crucial for unveiling novel properties of quantum many-body systems. A prominent example is the enhanced scattering between electrons and magnetic impurities in the low-energy limit, which gives rise to the Kondo effect. In this letter, motivated by recent developments in quantum simulation platforms, we investigate the universal behavior of long-range quantum spin chains with a single local impurity, focusing on systems that conserve the magnon number. Using effective field theory, we show that distinct classes of universal three-magnon states can emerge when the impurity-mediated two-magnon interaction is on resonance. When the long-range coupling decays as 1/rα1/r^α1/rα, we find that (i) for α∈(2,2.89)α\in (2,2.89)α∈(2,2.89), the system exhibits Efimov effects, with the three-body binding energy forming a geometric series ln⁡∣E3-body(n)∣∼−n(α−1)π/s0(α)\ln|E^{(n)}_{\text{3-body}}|\sim-n (α-1) π/s_0(α)ln∣E3-body(n)​∣∼−n(α−1)π/s0​(α), (ii) for α=2α=2α=2, the system shows semi-super Efimov effects with ln⁡∣E3-body(n)∣∼−(nπ−θ)2/8\ln|E^{(n)}_{\text{3-body}}|\sim-(nπ-θ)^2/8ln∣E3-body(n)​∣∼−(nπ−θ)2/8. Our theoretical prediction is validated by the numerical solution of the Skorniakov-Ter-Martirosian equation. Our results could be tested experimentally in the future on quantum simulation platforms.
Understanding the emergence of novel collective behaviors in strongly interacting systems lies at the heart of quantum many-body physics. Valuable insight comes from examining how few-body correlations manifest in many-body systems, embodying the ``from few to many'' philosophy. An intriguing example is the set of universal relations in ultracold atomic gases, which connect a wide range of observables to a single quantity known as the contact. In this Letter, we demonstrate that universal relations manifest in a distinct class of quantum many-body systems, long-range quantum spin chains, which belong to a completely new universality class. Using effective field theory and the operator product expansion, we establish connections between the asymptotic behavior of equal-time spin correlation functions, the dynamical structure factor, and the contact density. The theoretical predictions for equal-time correlators are explicitly verified through numerical simulations based on matrix product states. Our results could be readily tested in state-of-the-art trapped-ion systems.
The Efimov effect was first predicted for three particles interacting at an sss-wave resonance in three dimensions. A subsequent study showed that the same effect can be realized by considering two-body and three-body interactions in mixed dimensions. In this work, we consider the three-body problem of two bosonic AAA atoms interacting with another single BBB atom in mixed dimensions: The AAA atoms are confined in a space of dimension dA{d}_{A}dA​ and the BBB atom in a space of dimension dB{d}_{B}dB​, and there is an interspecies sss-wave interaction in a dint{d}_{\mathrm{int}}dint​-codimensional space accessible to both species. We find that when the sss-wave interaction is tuned on resonance, there emerge an infinite series of universal three-body bound states for dA,dB,dint=2,2,0{{d}_{A},{d}_{B},{d}_{\mathrm{int}}}={2,2,0}dA​,dB​,dint​=2,2,0 and 2,3,1{2,3,1}2,3,1. Going beyond the Efimov paradigm, the binding energies of these states follow the scaling $ln|{E}_{n}{|\ensuremath{\sim}\ensuremath{-}s(n\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta})}^{2}/4$, with the scaling factor sss being unity for the former case and mB(2mA+mB)/(mA+mB)\sqrt{{m}_{B}(2{m}_{A}+{m}_{B})}/({m}_{A}+{m}_{B})mB​(2mA​+mB​)​/(mA​+mB​) for the latter. We discuss the possibility of realizing our mixed-dimensional systems in a cold-atom experiment and how the effects of these universal three-body bound states may be detected.
Three interacting particles form a system which is well known for its complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of weakly bound trimer states appearing for three identical bosons with a resonant two-body interaction. Surprisingly, these states even exist in the absence of a corresponding two-body bound state and their precise nature is largely independent of the particular type of the two-body interaction potential. Efimov's scenario has attracted great interest in many areas of physics; an experimental test however has not been achieved. We report the observation of an Efimov resonance in an ultracold thermal gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths and arises from the coupling of three free atoms to an Efimov trimer. We observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied near a Feshbach resonance. This resonance develops into a continuum resonance at non-zero collision energies, and we observe a shift of the resonance position as a function of temperature. We also report on a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point from which to explore the universal properties of resonantly interacting few-body systems.
The Efimov phenomenon manifests itself as an emergent discrete scaling symmetry in the quantum three-body problem. In the unitarity limit, it leads to an infinite tower of three-body bound states with energies forming a geometric sequence. In this work, we study the evolution of these so-called Efimov states using relativistic scattering theory. We identify them as poles of the three-particle SSS matrix in the complex energy plane, and we study how they transform from virtual states through bound states to resonances when we change the interaction strength. We dial the scattering parameters toward the unitarity limit and observe the emergence of the universal scaling of energies and couplings---a behavior known from the nonrelativistic case. We additionally find that Efimov resonances follow unusual, cyclic trajectories accumulating at the three-body threshold and then disappear at some values of the two-body scattering length. We propose a partial resolution to this ``missing states'' problem.
Universal behavior has been found inside the window of Efimov physics for systems with N=4,5,6N=4,5,6N=4,5,6 particles. Efimov physics refers to the emergence of a number of three-body states in systems of identical bosons interacting via a short-range interaction becoming infinite at the verge of binding two particles. These Efimov states display a discrete scale invariance symmetry, with the scaling factor independent of the microscopic interaction. Their energies in the limit of zero-range interaction can be parametrized, as a function of the scattering length, by a universal function. We have found, using the form of finite-range scaling introduced by A. Kievsky and M. Gattobigio [Phys. Rev A 87, 052719 (2013)], that the same universal function can be used to parametrize the ground and excited energy of $N\ensuremath{\le}6$ systems inside the Efimov-physics window. Moreover, we show that the same finite-scale analysis reconciles experimental measurements of three-body binding energies with the universal theory.