Shimpei Endo

Neural-network quantum states have been developed as an efficient method for solving quantum many-body problems, not only in lattice systems but also in systems of particles in continuous space. Here, we apply this approach to strongly interacting few-body problems in continuous space at unitarity: the Efimov states and associated few-body bound states. We extend the previous work [], in which the ground states of few-boson systems were obtained, to the first excited states with a projection method, and also to a mass-imbalanced fermionic system consisting of two identical fermions and a third particle. The obtained energies of the ground and first excited states of these systems agree well with previously reported results. Furthermore, the proposed approach also reproduces the discrete scale invariance between the ground and first excited states and the critical-mass behavior in mass-imbalanced fermionic systems.

We study the Schrödinger equation with 1 / r 3 and attractive 1 / r 2 potentials. Using the quantum defect theory, we obtain analytical solutions for both repulsive and attractive 1 / r 3 interactions. The obtained discrete-scale-invariant energies and wave functions, validated by excellent agreement with numerical results, provide a natural framework for describing the universality of Efimov states in mixed dimension. Specifically, we consider a three-body system consisting of two heavy particles with large dipole moments confined to a quasi-one-dimensional geometry and resonantly interacting with an unconfined light particle. With the Born-Oppenheimer approximation, this system is effectively reduced to the Schrödinger equation with 1 / r 3 and 1 / r 2 potentials, and manifests the Efimov effect. Our analytical solution suggests that, for repulsive dipole interactions, the three-body parameter of the mixed-dimensional Efimov states is universally set by the dipolar length scale, whereas for attractive interactions it explicitly depends on the short-range phase. We also investigate the effects of finite transverse confinement and find that our analytical results are useful for describing the Efimov states composed of two polar molecules and a light atom.

Universality in physics describes the emergence of common features in vastly different systems. One fascinating example is the Efimov phenomenon where three-body resonantly interacting systems display universal properties. Efimov states have been observed in ultra-cold-atom systems, but their manifestation in nuclei remains elusive due to the long-range repulsive Coulomb interaction and the stringent requirement for at least two s-wave resonances in its subsystems. Recent theories propose another universality in three-body halos with only one s-wave resonance. Here, we report the identification of a precursor of this phenomenon in a neutron-rich ¹⁰He nucleus. With higher statistics and better sensitivities than previous experiments, we identify two low-lying 0⁺ states of ¹⁰He at ~ 1 MeV and ~ 2 MeV above its two-neutron decay threshold, and determine an s-wave scattering length of ~ - 3.5 fm between ⁸He and neutron. It is revealed that the lower energy state, the ground state of ¹⁰He, is a three-body state with only s-wave interactions among its subsystems. This state manifests as a resonance structure, which is a direct consequence of a universal long-range three-body repulsion. Our work sheds new light on quantum halos with finite lifetimes, providing a path toward their unified understanding across various scales and fields.

We study the Efimov states in highly mass-imbalanced three-body systems composed of two identical heavy atoms and one light atom, focusing on the Er-Er-Li and Dy-Dy-Li cold-atom mixtures with strong dipole-dipole interactions between the heavy atoms. By solving the Born-Oppenheimer equation for varying s -wave scattering lengths between the heavy and light atoms, we demonstrate for both bosonic and fermionic systems that the Efimov spectra and hence the three-body parameters are universal even with the dipole interaction comparable in strength to the van der Waals interaction. While the bosonic systems exhibit Efimov states only in the M z = 0 channel, the fermionic systems show a characteristic doublet of the Efimov states in the M z = 0 and M z = ± 1 channels due to the interplay of finite angular momentum and the anisotropy of the dipole interaction. Both numerical results and analytical formulas obtained with the first-order perturbation show that the ratio of the three-body parameters between these two fermionic channels exhibits universality, particularly well in the limit of large mass imbalance. Leveraging this universality, we provide quantitative predictions for the values and ratios of the three-body parameters for experimentally relevant Er-Li and Dy-Li isotopes.

Symmetry breaking underlies diverse phenomena from phase transitions in condensed matter to fundamental interactions in gauge theories. Despite many proposed indicators, a general quantification of symmetry breaking that is faithful, computable, and valid in the thermodynamic limit has remained elusive. Here, within quantum resource theory, we propose the quantum Fisher information (QFI) as such a measure. We demonstrate its utility by computing QFI for paradigmatic models: in the BCS superconductor, the QFI counts the number of Cooper pairs; in the transverse-field XY spin chains, it captures topological phase transition that has no local order parameter; and in quantum quench dynamics, it allows us to exactly derive the microscopic origin and conditions of the quantum Mpemba effect in terms of excitation propagation, including in the thermodynamic limit--beyond the reach of previous analyses. Our results show that the QFI, which is a complete resource monotone in the resource theory of asymmetry that plays the role of entanglement entropy in entanglement theory, faithfully captures symmetry breaking in condensed-matter systems. These results highlight the QFI as a universal and physically meaningful diagnostic of symmetry breaking in both equilibrium and non-equilibrium quantum many-body systems.

This review article presents historical developments and recent advances in our understanding on the three-body forces and Efimov physics, from an interdisciplinary viewpoint encompassing nuclear physics and cold atoms. Theoretical attempts to elucidate the three-body force with the chiral effective field theory are explained, followed by an overview of experiments aimed at observing signatures of the nuclear three-body force. Some recent experimental and theoretical works in the field of cold atoms devoted to measuring and engineering three-body forces among atoms are also presented. As a phenomenon arising from the three-body effect, Efimov physics in both cold atoms and nuclear systems is reviewed.