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Neural-network quantum states for solving few-body problems: Application to Efimov physics

Sora Yokoi, Shimpei Endo*, and Hiroki Saito†

  • *Contact author: shimpei.endo@uec.ac.jp
  • †Contact author: hiroki.saito@uec.ac.jp
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Phys. Rev. Research 8, 033335 – Published 18 September, 2026

DOI: https://doi.org/10.1103/31mv-7tz7

Abstract

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 [J. Phys. Soc. Jpn. 87, 074002 (2018)], 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.

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Phys. Rev. Research 8, 033335– Published 18 September, 2026
  • Received 5 April 2026
  • Accepted 28 August 2026
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