Composite-fermion description of rotating Bose gases at low angular momenta

TL;DR

This paper explores the composite fermion approach to rotating Bose gases at low angular momenta, revealing that the CF wave function becomes exact at a specific state in the large particle limit, indicating a new mathematical identity.

Contribution

It introduces a novel method for managing derivatives in the CF wave function and demonstrates its exactness at a particular state in the large N limit, extending CF theory to low angular momentum regimes.

Findings

CF wave function at L=N becomes exact as N grows large

New method for handling derivatives in CF wave functions

Mathematical identity relevant to low angular momentum regimes

Abstract

We study the composite fermion construction at and below the single vortex ($L=N$) state of weakly interacting rotating Bose gases, presenting a new method for handling the large number of derivatives typically occurring via the Slater determinant. Remarkably, the CF wave function at $L=N$ becomes {\em exact} in the large $N$ limit, even though this construction is not, {\em a priori}, expected to work in the low angular momentum regime. This implies an interesting mathematical identity which may be useful in other contexts.