Quantal molecular description and universal aspects of the spectra of bosons and fermions in the lowest Landau level

Abstract

Through the introduction of a class of trial wave functions portraying combined rotations and vibrations of molecules formed through particle localization in concentric polygonal rings, a correlated basis is constructed that spans the translationally invariant part of the lower-Landau-level (LLL) spectra. These trial functions, referred to as rovibrational molecular (RVM) functions, generalize our previous work which focused exclusively on electronic cusp states, describing them as pure vibrationless rotations. From a computational viewpoint, the RVM correlated basis enables controlled and systematic improvements of the original strongly-correlated variational wave function. Conceptually, it provides the basis for the development of a quantal molecular description for the full LLL spectra. 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. Furthermore, it follows that all other translationally invariant trial functions (e.g., the Jastrow-Laughlin, compact composite-fermion, or Moore-Read functions) are reducible to a description in terms of an excited rotating/vibrating quantal molecule.

Revtex4. 17 pages with 4 figures and 8 Tables. To appear in Physical Review A. For related papers, see http://www.prism.gatech.edu/~ph274cy/

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• 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