Long-range Efimov states

Ning Sun, Lei Feng, Pengfei Zhang

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.

Miwae Yamazaki

Ludovic Pricoupenko

A filtering method is introduced for solving the zero-range three-boson problem. This scheme permits solving the original Skorniakov Ter-Martirosian integral equation for an arbitrary large ultraviolet cutoff and avoiding the Thomas collapse of the three particles. The method is applied to a more general zero-range model including a finite-background two-body scattering length and the effective range. A crossover in the Efimov spectrum is found in such systems and a specific regime emerges where Efimov states are long-lived.

Anonymous

S. Oryu

On the three-body kinematics, we investigate the threshold behavior which appears not only at the three-body break-up threshold (3BT), but also at the quasi two-body threshold (Q2T) for the reactions: $$A+(BC)\rightarrow A+B+C$$ , and $$(ABC)\rightarrow A+(BC)$$ , respectively. Recently, the author proposed a general particle $$ {transfer}$$ (GPT) potential which appears, not only at the 3BT, but also at the Q2T between A and (BC). The new potential indicates a Yukawa-type potential for short range, but a $$1/r^n$$ -type potential for long range. The long range part of the GPT potential for $$n=1$$ indicates an attractive Coulomb-like or a gravitation-like potential. While, $$n=2$$ indicates the Efimov-like potential between A and (BC). The three-body binding energy: $$E_n=\epsilon +\zeta _n$$ with the two-body binding energy $$\epsilon $$ , and the separation energy $$\zeta _n$$ for $$(ABC)\rightarrow A+(BC)$$ satisfies $$E_n/E_{n+1}=\zeta _n/\zeta _{n+1}$$ =const for $$\epsilon =0$$ or the two-body scattering length: $$a\rightarrow \infty $$ (i.e. the two-body unitary limit). At the Q2T, the condensation of the three-body binding energy is given by the GPT-potential in the form of $$E_n/E_{n+1}=(\zeta _n+\epsilon )/(\zeta _{n+1}+\epsilon )\rightarrow 1$$ (const) for $$n\rightarrow \infty $$ (with $$\zeta _n\rightarrow 0$$ ) which implies the existence of Efimov-like states at the Q2T in the hadron systems, thereby the possibility of “ultra low energy nuclear transformation”, where the three-body binding energies degenerate at zero energy. Finally, the origin of such a long range potential will be clarified.

Yiran Huo, Pengfei Zhang

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.