I am currently trying to understand the apparent equivalence between spin stiffness and superfluid density. I (think I) understand how the XXZ model maps onto the Boson-Hubbard model with the appropriate relabelling of operators and parameters. However, what I do not understand is the connection between superfluid density and spin stiffness. This relationship is alluded to many times, including in the wikipedia article on spin stiffness, but the mapping is never fully explained in terms I understand. This article (see bottom of page 27) talks a bit about how the superfluid density measures the response of the energy to a twist in boundary conditions, and I see how this relates to spin stiffness, but understanding how to interpret this quantity as a superfluid "density" is not immediately obvious to me. Thanks!
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