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arXiv:2507.04993 · Physical review. B./Physical review. B

Universal bound states in long-range spin chains with an impurity

Ning G. Sun, Lei Feng, Pengfei Zhang

Published Apr 7, 2026• 1 citation
arXivHTMLPDF

Abstract

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 $1/r^α$, we find that (i) for $α\in (2,2.89)$, the system exhibits Efimov effects, with the three-body binding energy forming a geometric series $\ln|E^{(n)}_{\text{3-body}}|\sim-n (α-1) π/s_0(α)$, (ii) for $α=2$, the system shows semi-super Efimov effects with $\ln|E^{(n)}_{\text{3-body}}|\sim-(nπ-θ)^2/8$. 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.

DOI
10.1103/c7lm-323v

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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.
We study the electron spin resonance in a dilute magnon gas that is realized in a ferromagnetic spin system at low temperature. A quantum cluster expansion is developed to show that the frequency shift of the single-magnon peak changes its sign and the linewidth reaches its maximum across a scattering resonance between magnons. Such characteristic behaviors are universal and can be used to experimentally locate the two-magnon resonance when an external parameter such as pressure is varied. Future achievement of the two-magnon resonance may have an impact comparable to the Feshbach resonance in ultracold atoms and will open up a rich variety of strongly correlated physics such as the recently proposed Efimov effect in quantum magnets. We also suggest how the emergence of an Efimov state of three magnons and its binding energy may be observed with the electron spin resonance.
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Small weakly bound droplets determine a number of properties of ultracold Bose and Fermi gases. For example, Efimov trimers near the atom-atom-atom and atom-dimer thresholds lead to enhanced losses from bosonic clouds. Generalizations to four- and higher-body systems have also been considered. Moreover, Efimov trimers have been predicted to play a role in the Bose polaron with large boson-impurity scattering length. Motivated by these considerations, the present work provides a detailed theoretical analysis of weakly bound NNN-body clusters consisting of $N\ensuremath{-}1$ identical bosons (denoted by ``B'') of mass mmm that interact with a single distinguishable impurity particle (denoted by ``X'') of mass MMM. The system properties are analyzed as a function of the mass ratio $\ensuremath{\kappa}$ (values from $\ensuremath{\kappa}=1$ to 50 are considered), where $\ensuremath{\kappa}$ is equal to m/Mm/Mm/M, and the two-body sss-wave scattering length aBX{a}_{\text{BX}}aBX​ between the bosons and the impurity. To reach the universal Efimov regime in which the size of the BBX trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: resonance states are determined in the absence of BB and BBX interactions, bound states are determined in the presence of repulsive three-body boson-boson-impurity interactions, and bound states are determined in the presence of repulsive two-body boson-boson interactions. The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.