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.
Highlights
The crossover from a fermionic superfluid of weakly bound Cooper pairs (BCS regime) to a Bose-Einstein condensate (BEC) of strongly bound dimers is a paradigmatic quantum many-body problem [1,2,3,4]
It was shown that measuring the position of all or at least a sufficiently large number of bosons in an yrast state reveals a dark-soliton-like particle depletion [30,33], and that wavepacket-like superpositions of yrast states emulate the behavior of classical dark solitons [31]
We focus on the yrast states around the maxima of the dispersion, which are related to dark solitons
Summary
The crossover from a fermionic superfluid of weakly bound Cooper pairs (BCS regime) to a Bose-Einstein condensate (BEC) of strongly bound dimers is a paradigmatic quantum many-body problem [1,2,3,4]. FCIQMC has been applied with great success to a large number of problems in this field [63,64] and recently to ultracold atoms [65,66] This method can find the ground-state energy and many-body wave function in a Fermi system by expanding the wave function into a set of Slater determinants.
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