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  • Open Access

Numerical tensor method for atomic and exotic three-particle systems

Kammegne Tcheugam Brice1, Michael Melgaard2, Marilia Pavlidou1, and Hazel Cox1,*

  • *Contact author: h.cox@sussex.ac.uk
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Phys. Rev. A 111, 022812 – Published 21 February, 2025

DOI: https://doi.org/10.1103/PhysRevA.111.022812

Abstract

In this paper we derive a numerical tensor method to solve the many-body Schrödinger equation for three-particle systems. The Schrödinger equation is first represented in a canonical tensor format using a triple orthogonal Laguerre-based wave function in scaled perimetric coordinates. We demonstrate that the antisymmetry of the wave function can be explicitly included in the tensor method formulation by coupling the indices associated with the coordinates representing the identical fermions, e.g., electrons or muons. It is shown that energies accurate to the picohartree can be achieved in full tensor format in less than 3300 s for atomic and muonic molecular systems. Furthermore, this CPU time is reduced to less than 300 s, without compromising the accuracy of the energy or quality of the wave function, using a low-rank tensor-train decomposition.

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References (44)

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Phys. Rev. A 111, 022812– Published 21 February, 2025
  • Received 6 December 2024
  • Accepted 3 February 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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