Asymptotically exact trial wave functions for yrast states of rotating Bose gases

TL;DR

This paper investigates the accuracy of composite fermion trial wave functions for rotating Bose gases, showing they closely approximate exact solutions at low angular momenta and providing analytical evidence for their convergence in the thermodynamic limit.

Contribution

The paper provides analytical methods and evidence demonstrating the convergence of composite fermion wave functions to exact solutions for yrast states at low angular momenta in rotating Bose gases.

Findings

Overlap between trial and exact wave functions increases with system size.

Strong evidence suggests overlaps approach unity in the thermodynamic limit.

Analytic structure of exact and trial wave functions shows remarkable similarity.

Abstract

We revisit the composite fermion (CF) construction of the lowest angular momentum yrast states of rotating Bose gases with weak short range interaction. For angular momenta at and below the single vortex, $L \leq N$, the overlaps between these trial wave functions and the corresponding exact solutions {\it increase} with increasing system size and appear to approach unity in the thermodynamic limit. In the special case $L=N$, this remarkable behaviour was previously observed numerically. Here we present methods to address this point analytically, and find strongly suggestive evidence in favour of similar behaviour for all $L \leq N$. While not constituting a fully conclusive proof of the converging overlaps, our results do demonstrate a striking similarity between the analytic structure of the exact ground state wave functions at $L \leq N$, and that of their CF counterparts. Results are given for two different projection methods commonly used in the CF approach.