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

TL;DR

This paper introduces rovibrational molecular (RVM) trial wave functions that provide a universal, quantal molecular framework for describing the spectra of bosons and fermions in the lowest Landau level, improving understanding of strongly correlated states.

Contribution

The paper develops a universal quantal molecular description for the entire lowest Landau level spectra, extending previous work and unifying various trial functions under this framework.

Findings

RVM functions form a correlated basis for LLL spectra

Universal applicability to bosons and fermions, yrast and excited states

All translationally invariant trial functions can be reduced to RVM descriptions

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.