The superfluid density in continuous and discrete spaces: Avoiding misconceptions

Abstract

We review the concept of superfluidity and, based on real and thought experiments, we use the formalism of second quantization to derive expressions that allow the calculation of the superfluid density for general Hamiltonians with path-integral methods. It is well known that the superfluid density can be related to the response of the free energy to a boundary phase-twist, or to the fluctuations of the winding number. However, we show that this is true only for a particular class of Hamiltonians. In order to treat other classes, we derive general expressions of the superfluid density that are valid for various Hamiltonians. While the winding number is undefined when the number of particles is not conserved, our general expressions allow us to calculate the superfluid density in all cases. We also provide expressions of the superfluid densities associated to the individual components of multi-species Hamiltonians, which remain valid when inter-species conversions occur. The cases of continuous and discrete spaces are discussed, and we emphasize common mistakes that occur when considering lattices with non-orthonormal primitive vectors.

11 figures

References in corpus (7)

• The Stochastic Green Function (SGF) algorithm
• Directed update for the Stochastic Green Function algorithm
• Feshbach-Einstein condensates
• Quantum phases of mixtures of atoms and molecules on optical lattices
• Comment on "Feshbach-Einstein Condensates" by V. G. Rousseau and P. J. H. Denteneer
• Drude weight, Meissner weight, rotational inertia of bosonic superfluids: how are they distinguished?
• Current Response in Extended Systems as a Geometric Phase: Application to Variational Wavefunctions

Cited by in corpus (16)

• Band geometry, Berry curvature and superfluid weight
• Pairing and superconductivity in the flat band: Creutz lattice
• Coherently driven microcavity-polaritons and the question of superfluidity
• Competing phases, phase separation and co-existence in the extended one-dimensional bosonic Hubbard model
• Staircase of crystal phases of hard-core bosons on the Kagome lattice
• Pairing and pair superfluid density in one-dimensional Hubbard models
• A quantum Monte Carlo study of the long-ranged site-diluted XXZ-model as realized by polar molecules
• Quantum Monte Carlo study of superfluid density in quasi-one-dimensional hard-core bosons: Effect of suppression of phase slippage
• Strain-induced superfluid transition for atoms on graphene
• Local Density of the Bose Glass Phase
• Self-Organized Bosonic Domain Walls
• Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects
• Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model
• Spatial distribution of superfluidity and superfluid distillation of Bose liquids
• The Bose-Hubbard model on a triangular lattice with diamond ring-exchange
• Ferromagnetic phase in the polarized two-species bosonic Hubbard Model