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. However, it remains an open question how analogous universal few-body physics can emerge in low-dimensional quantum platforms. In this work, 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 for the three-magnon problem, leading to the celebrated Efimov effect. 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. The Efimov effect is a quantum phenomenon in which three particles form an infinite series of low-energy bound states at resonance, previously observed in three-dimensional systems. The authors extend this celebrated effect to long-range quantum spin systems, demonstrating long-range spin chains can also host Efimov states with widely tunable scaling ratios controlled by the interaction range.
Sun et al. (Wed,) studied this question.