Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential

@article{Koscik2021PaircorrelationAF,
  title={Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential},
  author={Przemyslaw Ko'scik and Arkadiusz Kuro's and Adam Pieprzycki and Tomasz Sowi'nski},
  journal={Scientific Reports},
  year={2021},
  volume={11}
}
We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations have two-body nature. By construction, the proposed ansatz is exact in the noninteracting limit, exactly encodes boundary conditions forced by contact interactions, and gives full control on accuracy in the limit of infinite repulsions. We show its efficiency… Expand

Figures from this paper

References

SHOWING 1-10 OF 71 REFERENCES
Exact Diagonalization Techniques 529–544
  • (Springer, Berlin,
  • 2008
An exact diagonalization study
  • Phys. Rev. A 75, 013614
  • 2007
Interacting Fermions in One Dimension. II. Attractive Potential
The exact energies and wavefunctions for a system of (N − 1) one‐dimensional fermions all of the same spin and one fermion of the opposite spin are calculated in the large volume, finite densityExpand
Observation of Pauli Crystals.
TLDR
This work reports on the direct observation of the Pauli principle in a continuous system of up to six particles in the ground state of a two-dimensional harmonic oscillator, and finds so-called Pauli crystals as a manifestation of higher order correlations. Expand
A systematic interpolatory method for an impurity in a one-dimensional fermionic background
We explore a new numerical method for studying one-dimensional quantum systems in a trapping potential. We focus on the setup of an impurity in a fermionic background, where a single distinguishableExpand
Exactly Solvable System of One-Dimensional Trapped Bosons with Short- and Long-Range Interactions.
TLDR
A model of trapped bosons with contact interactions as well as Coulomb repulsion or gravitational attraction in one spatial dimension is introduced and the exact ground-state energy and many-body wave function is found. Expand
Variational ansatz for p-wave fermions confined in a one-dimensional harmonic trap
We propose a very accurate and efficient variational scheme for the ground state of the system of $p$-wave attractively interacting fermions confined in a one-dimensional harmonic trap. By theExpand
Efficient Construction of Many-Body Fock States Having the Lowest Energies
To perform efficient many-body calculations in the framework of the exact diagonalization of the Hamiltonian one needs an appropriately tailored Fock basis built from the single-particle orbitals.Expand
One-dimensional mixtures of several ultracold atoms: a review.
TLDR
The recent advances on trapped Bose-Fermi mixtures are described, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Expand
Phase-separation dynamics induced by an interaction quench of a correlated Fermi-Fermi mixture in a double well
We explore the interspecies interaction quench dynamics of ultracold spin-polarized few-body mass balanced Fermi-Fermi mixtures confined in a double-well with an emphasis on the beyond Hartree-FockExpand
...
1
2
3
4
5
...