Signatures of the BCS-BEC crossover in the yrast spectra of Fermi quantum rings

TL;DR

This paper investigates the evolution of the lowest energy states with non-zero momentum in attractive Fermi systems on quantum rings, revealing how dimensional crossover and pairing influence the excitation spectra and indicating fragmented condensation phenomena.

Contribution

It combines Bethe ansatz and Quantum Monte Carlo methods to analyze the BCS-BEC crossover in Fermi quantum rings, highlighting spectral changes and condensed state signatures.

Findings

Yrast spectra evolve from 1D to 2D regimes

Pairing significantly alters excitation spectra

Fragmented condensation signatures observed in certain states

Abstract

We study properties of the lowest energy states at non-zero total momentum (yrast states) of the Hubbard model for spin-1/2 fermions in the quantum ring configuration with attractive on-site interaction at low density. In the one-dimensional (1D) case we solve the Hubbard model using the Bethe ansatz, while for the crossover into the 2D regime we use the Full-Configuration-Interaction Quantum Monte-Carlo method (FCIQMC) to obtain the yrast states for the spin-balanced Fermi system. We show how the yrast excitation spectrum changes from the 1D to the 2D regime and how pairing affects the yrast spectra. We also find signatures of fragmented condensation for certain yrast states usually associated with dark solitons.