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

TL;DR

This study uses exact diagonalization to analyze rotating boson molecules with short or long-range interactions, revealing their crystalline structures, rotational behaviors, and dependence on fractional filling in small bosonic systems.

Contribution

It provides a detailed characterization of rotating boson molecules, showing their formation, angular momentum steps, and the influence of fractional filling and interaction range on their crystalline correlations.

Findings

Bosons localize into rotating molecules with concentric rings.

Ground-state angular momenta increase in steps matching boson counts per ring.

Crystalline correlations depend more on fractional filling than interaction range.

Abstract

The Hamiltonian for a small number, N <= 11, 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 diagonalization in the lowest Landau level. Our analysis shows that, for both low and high fractional fillings, the bosons localize and form rotating boson molecules (RBMs) consisting of concentric polygonal rings. Focusing on systems with the number of trapped atoms sufficiently large to form multi-ring bosonic molecules, we find that, as a function of the rotational frequency and regardless of the type of repulsive interaction, the ground-state angular momenta grow in specific steps that coincide with the number of localized bosons on each concentric ring. Comparison of the conditional probability distributions (CPDs) for both interactions suggests that the degree of crystalline correlations appears to depend more on the fractional filling nu than on the range of the interaction. The RBMs behave as nonrigid rotors, i.e., the concentric rings rotate independently of each other. At filling fractions nu < 1/2, we observe well developed crystallinity in the CPDs (two-point correlation functions). For larger filling fractions nu > 1/2, observation of similar molecular patterns requires consideration of even higher-order correlation functions.