A fully quantal molecular description for the spectra of bosons and fermions in the lowest Landau level

Abstract

Through the introduction of a class of appropriate translationally invariant trial wave functions, we show that the strong correlations in the lowest Landau level (LLL) reflect in finite systems the emergence of intrinsic point-group symmetries associated with rotations and vibrations of molecules formed through particle localization. This quantal molecular description is universal, being valid for both bosons and fermions, for both the yrast and excited states of the LLL spectra, and for both low and high angular momenta. "Quantum-fluid" physical pictures associated with Jastrow-type trial functions are shown to be reducible to the molecular description introduced in this paper.

REVTEX 4. 6 pages with 1 color figure and 3 Tables. An extended version [15 pages] was published as Phys. Rev. A 81, 023609 (2010); see http://arxiv.org/abs/1001.1090. For other related papers, see http://www.prism.gatech.edu/~ph274cy/

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• Vortices in quantum droplets: Analogies between boson and fermion systems
• Unified microscopic approach to the interplay of pinned-Wigner-solid and liquid behavior of lowest-Landau-level states in the neighborhood of nu=1/3
• Fractional quantum Hall physics and higher-order momentum correlations in a few spinful fermionic contact-interacting ultracold atoms in rotating traps
• Edge and bulk components of lowest-Landau-level orbitals, correlated fractional quantum Hall effect incompressible states, and insulating behavior in finite graphene samples
• Ground and Low-Lying Collective States of Rotating Three-Boson System
• Interacting electrons in a magnetic field in a center-of-mass free basis
• Wave-function microscopy: Derivation and anatomy of exact algebraic spinful wave functions and full Wigner-molecular spectra of a few highly correlated rapidly rotating ultracold fermionic atoms
• Artificial versus Natural Atoms: The uncanny capability of the many-body Schrödinger equation to produce emergent behavior