Universality of Many-Body States in Rotating Bose and Fermi Systems

TL;DR

This paper introduces a universal transformation linking bosonic and fermionic many-body states in rotating systems, demonstrating high overlaps at extreme angular momenta and exploring the complexities at intermediate values.

Contribution

It proposes a new universal transformation inspired by Laughlin and Jain wave functions, enabling comparison of bosonic and fermionic states in rotating quantum systems.

Findings

High overlap (>90%) at small and high angular momenta

Complex state mixing reduces overlap at intermediate angular momenta

Transformation effectively connects bosonic and fermionic states in the lowest Landau level

Abstract

We propose a universal transformation from a many-boson state to a corresponding many-fermion state in the lowest Landau level approximation of rotating many-body systems, inspired by the Laughlin wave function and by the Jain composite-fermion construction. We employ the exact-diagonalization technique for finding the many-body states. The overlap between the transformed boson ground state and the true fermion ground state is calculated in order to measure the quality of the transformation. For very small and high angular momenta, the overlap is typically above 90%. For intermediate angular momenta, mixing between states complicates the picture and leads to small ground-state overlaps at some angular momenta.