Pairing and pair superfluid density in one-dimensional Hubbard models

TL;DR

This study uses advanced computational methods to analyze pair superfluidity in one-dimensional Hubbard models, revealing that pairs dominate superfluidity for any attraction, with significant implications for understanding superfluid behavior.

Contribution

The paper demonstrates the one-to-one correspondence between Drude weight tensor and winding numbers, and clarifies the pair-only nature of superfluidity in 1D Hubbard models with attractive interactions.

Findings

Pairs form and dominate superfluidity for any nonzero attraction.

Weak attraction leads to exponentially diverging pair size, resembling BCS pairing.

Superfluidity in bosons is also due solely to pairs, even at minimal attraction.

Abstract

We use unbiased computational methods to elucidate the onset and properties of pair superfluidity in two-species fermionic and bosonic systems with onsite interspecies attraction loaded in one-dimensional optical lattice. We compare results from quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG), emphasizing the one-to-one correspondence between the Drude weight tensor, calculated with DMRG, and the various winding numbers extracted from the QMC. Our results show that, for any nonvanishing attractive interaction, pairs form and are the sole contributors to superfluidity, there are no individual contributions due to the separate species. For weak attraction, the pair size diverges exponentially, i.e. Bardeen-Cooper-Schrieffer (BCS) pairing requiring huge systems to bring out the pair-only nature of the superfluid. This crucial property is largely overlooked in many studies, thereby misinterpreting the origin and nature of the superfluid. We compare and contrast this with the repulsive case and show that the behavior is very different, contradicting previous claims about drag superfluidity and the symmetry of properties for attractive and repulsive interactions. Finally, our results show that the situation is similar for soft core bosons: superfluidity is due only to pairs, even for the smallest attractive interaction strength compatible with the largest system sizes that we could attain.