Abstract
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 $0 \leq S \leq N/2$ in the neighborhood of the $\nu=1$ filling, covering the range from the maximum density droplet to the first quasihole. Our theoretical predictions for higher-order spatial and momentum correlations reveal intrinsic polygonal, multi-ring crystalline-type structures, which can be tested with ultracold-atom experiments in rapidly rotating traps, simulating quantum Hall physics (including quantum LLL skyrmions).
Highlights
Exact analytic solutions for the quantum many-body problem, whether in a closed-form algebraic expression or in the form of the Bethe ansatz, are highly coveted and soughtafter; they are available only for a few cases
We first introduce an approach for the extraction of exact analytic wave functions (EAWFs) from the digital information provided via numerical exact-diagonalization of the many-body LLL Hamiltonian
The compact EAWFs enable consideration of larger assemblies compared to the CI-computed ultracold Wigner molecules (UCWMs) [38]
Summary
Exact analytic solutions for the quantum many-body problem, whether in a closed-form algebraic expression or in the form of the Bethe ansatz, are highly coveted and soughtafter; they are available only for a few cases We derive closed-form exact analytic wave functions (EAWFs) for two-dimensional (2D) systems of spinful contact-interacting lowest-Landau-level (LLL) fermions that simulate fractional quantum Hall (FQH) physics [32,33,34,35,36,37,38,39] with trapped ultracold atoms.
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