Pairing and pair superfluid density in one-dimensional Hubbard models

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 onedimensional 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.

Collisionless drag for a one-dimensional two-component Bose-Hubbard model

“…Note added: while completing the present work we became aware of a DMRG-QMC comparison for the study of the pairing properties of one-dimensional hardcore bosons [36]. The results show the slow convergence to the thermodynamic limit for the spin-channel as in our soft-core case.…”

Superfluidity in the 1D Bose-Hubbard Model

“…A popular approach in the QMC community is to exploit an identity between the superfluid density and the imaginary-time winding number [37]. DMRG techniques have been used to calculate the superfluid density in finite-length systems by imposing a phase twist to systems with open boundary conditions [19,38], or periodic boundary conditions [27,39]. Our numerical method has some advantages over these prior approaches: We minimize the energy within the space of translationallyinvariant matrix product states, directly giving us results in the zero temperature and thermodynamic limit.…”