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

TL;DR

This paper extends neural-network quantum states to continuous few-body problems, successfully computing Efimov states and bound states, demonstrating accuracy and capturing key Efimov features.

Contribution

The authors develop a neural-network approach for continuous-space few-body problems, accurately computing states and reproducing Efimov physics features.

Findings

Accurately computed ground and excited states for 3-6 bosons at unitarity.

Reproduced Efimov states' discrete scale invariance and geometric wave function structure.

Validated approach on mass-imbalanced fermionic systems.

Abstract

Neural-network quantum states have recently emerged as a powerful method for solving quantum many-body problems, with notable successes in lattice systems. Here, we extend this approach to strongly interacting few-body problems in continuous space, and demonstrate its capability by computing the Efimov states and associated few-body bound states. Using a fully connected feedforward neural network with Jacobi coordinates as inputs, combined with a projection method, we compute the ground and first excited states for three- to six-body systems of identical bosons at unitarity, as well as a mass-imbalanced fermionic system consisting of two identical fermions and a third particle. The obtained energies of the ground and first excited states agree well with previously reported results. Furthermore, the proposed approach also reproduces key features of Efimov states, including the discrete scale invariance, the characteristic geometric structure of the wave function, and the critical-mass behavior in mass-imbalanced fermionic systems. Our method can be readily applied to a broad class of strongly correlated few-body problems in continuous space.