Ning Sun

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.

When two non-relativistic particles interact resonantly in three dimensions, an infinite tower of three-body bound states emerges, exhibiting a discrete scale invariance. This universal phenomenon, known as the Efimov effect, has garnered extensive attention across various fields, including atomic, nuclear, condensed matter, and particle physics. In this letter, we demonstrate that the Efimov effect also manifests in long-range quantum spin chains. The long-range coupling modifies the low-energy dispersion of magnons, enabling the emergence of continuous scale invariance for two-magnon states at resonance. This invariance is subsequently broken to discrete scale invariance upon imposing short-range boundary conditions for the three-magnon problem, leading to the celebrated Efimov bound states. Using effective field theory, we theoretically determine how the ratio of two successive binding energies depends on the interaction range, which agrees with the numerical solution of the bound-state problem. We further discuss generalizations to arbitrary spatial dimensions, where the traditional Efimov effect serves as a special case. Our results reveal universal physics in dilute quantum gases of magnons that can be experimentally tested in trapped-ion systems.