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Contactium: A strongly correlated model system.

Jerzy Cioslowski1, Berthold-Georg Englert2,3,4, Martin-Isbjörn Trappe2

  • 1Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.

The Journal of Chemical Physics
|May 12, 2023
PubMed
Summary
This summary is machine-generated.

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The study reveals unique properties of strongly correlated two-particle systems in harmonic confinement, showing all natural orbitals remain occupied and exhibit distinct behaviors compared to Coulombic systems.

Area of Science:

  • Quantum mechanics
  • Atomic physics
  • Condensed matter theory

Background:

  • Strongly correlated quantum systems are crucial for understanding complex many-body phenomena.
  • Harmonic confinement and contact interactions offer a simplified yet non-trivial model for studying quantum correlations.
  • Conventional models often rely on Coulombic interactions, limiting insights into alternative interaction potentials.

Purpose of the Study:

  • To analyze the one-particle description of two fermions or bosons in harmonic confinement with Fermi-Huang pseudopotential interaction at infinite confinement strength.
  • To identify and characterize peculiarities of this system, termed "contactium," in contrast to conventional Coulombic systems.
  • To investigate the properties of natural orbitals (NOs) and occupation numbers in the contactium model.

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Main Methods:

  • Analysis of the ground state properties at the limit of infinite confinement strength (ω → ∞).
  • Detailed examination of the one-particle description, including natural orbitals (NOs) and occupation numbers.
  • Comparison of contactium properties with conventional systems like the two-electron harmonium atom.

Main Results:

  • In the contactium, all natural orbitals (NOs) remain occupied, implying nonzero collective occupancies for all angular momenta.
  • NOs and occupation numbers {νn} relate to eigenfunctions/eigenvalues of a zero-energy Schrödinger equation with an attractive Gaussian potential.
  • Distinct asymptotic decays for occupation numbers (n⁻⁴/³) and kinetic energy contributions (n⁻²/³) were derived, differing from Coulombic systems (n⁻⁸/³).
  • Weakly occupied NOs of the contactium, upon scaling, resemble those of the two-electron harmonium atom at ω → ∞.

Conclusions:

  • The "contactium" model exhibits unique quantum correlation behaviors not seen in Coulombic systems.
  • The mathematical relationship between NOs and Gaussian potentials provides a powerful tool for analyzing these systems.
  • Despite differing interactions, the contactium shares asymptotic similarities with Coulombic systems in the high-confinement limit, suggesting universal aspects of quantum correlations.