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

TL;DR

This paper derives exact closed-form wave functions for contact-interacting spinful fermions in two dimensions under rapid rotation, revealing crystalline structures that can be tested in ultracold atom experiments simulating quantum Hall effects.

Contribution

It provides the first explicit analytic wave functions for arbitrary numbers of contact-interacting spinful fermions in 2D at specific angular momenta near the quantum Hall regime.

Findings

Revealed intrinsic polygonal, multi-ring crystalline structures in the wave functions.

Predicted spatial and momentum correlations testable in ultracold atom experiments.

Connected wave function structures to quantum Hall phenomena like skyrmions.

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).