# Exact closed-form analytic wave functions in two dimensions: Contact-interacting fermionic spinful ultracold atoms in a rapidly rotating trap

@inproceedings{Yannouleas2021ExactCA, title={Exact closed-form analytic wave functions in two dimensions: Contact-interacting fermionic spinful ultracold atoms in a rapidly rotating trap}, author={Constantine Yannouleas and Uzi Landman}, year={2021} }

Exact two-dimensional analytic wave functions for an arbitrary number N of contact-interacting lowest-Landau-level (LLL) spinful fermions are derived with the use of combined numerical and symbolic computational approaches via analysis of exact Hamiltonian numerical diagonalization data. Closed-form analytic expressions are presented for two families of zero-interaction-energy states at given total angular momentum and total spin 0 ≤ S ≤ N/2 in the neighborhood of the ν = 1 filling, covering… Expand

#### References

SHOWING 1-10 OF 95 REFERENCES

Exact solution for infinitely strongly interacting Fermi gases in tight waveguides.

- Physics, Medicine
- Physical review letters
- 2009

It is shown that the total ground-state density profile behaves like the polarized noninteracting fermions, whereas the spin-dependent densities display different properties for different spin configurations. Expand

Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential

- Physics, Medicine
- Science Advances
- 2015

This work proposes a powerful ansatz for the one-dimensional Fermi gas in a harmonic potential near the limit of infinite short-range repulsion, and shows that the classical Pascal’s triangle emerges in the expression for the ground-state wave function. Expand

Trial wave functions with long-range Coulomb correlations for two-dimensional N-electron systems in high magnetic fields

- Physics
- 2002

A new class of analytic wave functions is derived for two dimensional N-electron $(2l~Nl\ensuremath{\infty})$ systems in high magnetic fields. These functions are constructed through breaking (at the… Expand

Rapidly rotating boson molecules with long- or short-range repulsion: An exact diagonalization study

- Physics
- 2007

The Hamiltonian for a small number N11 of bosons in a rapidly rotating harmonic trap, interacting via a short range contact potential or a long range Coulomb interaction, is studied via an exact… Expand

Hard-wall confinement of a fractional quantum Hall liquid

- Physics
- 2017

We make use of numerical exact diagonalization calculations to explore the physics of $\nu = 1/2$ bosonic fractional quantum Hall (FQH) droplets in the presence of experimentally realistic… Expand

Bosonic molecules in rotating traps.

- Physics, Medicine
- Physical review letters
- 2006

We present a variational many-body wave function for repelling bosons in rotating traps, focusing on rotational frequencies that do not lead to restriction to the lowest Landau level. This wave… Expand

Two-dimensional quantum dots in high magnetic fields: Rotating-electron-molecule versus composite-fermion approach

- Physics
- 2003

Exact diagonalization results are reported for the lowest rotational band of $N=6$ electrons in strong magnetic fields in the range of high angular momenta, $70l~Ll~140$ (covering the corresponding… Expand

Quantum Hall Phases and Plasma Analogy in Rotating Trapped Bose Gases

- Physics, Mathematics
- 2014

A bosonic analogue of the fractional quantum Hall effect occurs in rapidly rotating trapped Bose gases: There is a transition from uncorrelated Hartree states to strongly correlated states such as… Expand

Single-atom-resolved probing of lattice gases in momentum space

- Physics
- 2018

Measuring the full distribution of individual particles is of fundamental importance to characterize many-body quantum systems through correlation functions at any order. Here we demonstrate the… Expand

Soluble models of strongly interacting ultracold gas mixtures in tight waveguides.

- Physics, Medicine
- Physical review letters
- 2007

A Fermi-Bose mapping method is used to determine the exact ground states of several models of mixtures of strongly interacting ultracold gases in tight waveguides, which are generalizations of the… Expand