Variational ansatz for p-wave fermions confined in a one-dimensional harmonic trap

@article{Koscik2020VariationalAF,
  title={Variational ansatz for p-wave fermions confined in a one-dimensional harmonic trap},
  author={Przemyslaw Ko'scik and Tomasz Sowi'nski},
  journal={arXiv: Quantum Gases},
  year={2020}
}
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 the construction, the method takes the non-analytical part of interactions exactly into account and thus it approximates the true ground-state wave function in a whole range of interactions very accurately. Within the method, we determine different properties of the system for a different number of particles… 
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TLDR
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.

References

SHOWING 1-10 OF 54 REFERENCES
Test of an Optimised Exact-Diagonalization Approach for Trapped Fermionic Mixtures
We probe the convergence of the configuration interaction (CI) approach for harmonically trapped one-dimensional Fermi–Fermi mixtures. Existing scientific papers that apply the CI approach to study
Scaling behavior of Tan's contact for trapped Lieb-Liniger bosons: From two to many
We show that the contact parameter of N harmonically-trapped interacting 1D bosons at zero temperature can be analytically and accurately obtained by a simple rescaling of the exact two-boson
Solutions of the Schrodinger equation for an attractive 1/r 6 potential
Mathematical methods are presented that give pairs of linearly independent solutions for an attractive ${1/r}^{6}$ potential. These solutions represent a different class of special functions that are
THE STRUCTURE OF FERMION DENSITY MATRICES
Abstract : A new approach is presented to the many-particle problem in quantum mechanics by proposing a method of finding natural orbitals and natural geminals of a system without prior knowledge of
TWO ONE-DIMENSIONAL INTERACTING PARTICLES IN A HARMONIC TRAP
In this brief report, two one-dimensional interacting particles interacting with a delta interaction in a harmonic trap is discussed. For strong interactions, we derive the asymptotic expressions for
Harmonic oscillator with a δ-function potential
Harmonic oscillator with a δ-function potential is analysed and compact expressions are obtained for the energy eigenvalues of the even parity states. These energies tend to the energy eigenvalues of
Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension
A rigorous one‐one correspondence is established between one‐dimensional systems of bosons and of spinless fermions. This correspondence holds irrespective of the nature of the interparticle
EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE
A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the
Quantum many body problem in one-dimension: Ground state
We investigate the ground state of a system of either fermions or bosons interacting in one dimension by a 2‐body potential V(r) = g/r2. In the thermodynamic limit, we determine the ground state
Entanglement between two interacting atoms in a one-dimensional harmonic trap
We investigate quantum entanglement properties between two interacting atoms in a one-dimensional harmonic trap. We provide detailed results for the dependencies of atom-atom entanglement on the
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