Universal Bound States in Long-range Spin Chains with an Impurity

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

6 pages, 2 figures

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Cited by in corpus (1)

• Universal Relations in Long-range Quantum Spin Chains