Path-integral computation of superfluid densities

E. L. Pollock, D. M. Ceperley

Research output: Contribution to journalArticlepeer-review


The normal and superfluid densities are defined by the response of a liquid to sample boundary motion. The free-energy change due to uniform boundary motion can be calculated by path-integral methods from the distribution of the winding number of the paths around a periodic cell. This provides a conceptually and computationally simple way of calculating the superfluid density for any Bose system. The linear-response formulation relates the superfluid density to the momentum-density correlation function, which has a short-ranged part related to the normal density and, in the case of a superfluid, a long-ranged part whose strength is proportional to the superfluid density. These facts are discussed in the context of path-integral computations and demonstrated for liquid He4 along the saturated vapor-pressure curve. Below the experimental superfluid transition temperature the computed superfluid fractions agree with the experimental values to within the statistical uncertainties of a few percent in the computations. The computed transition is broadened by finite-sample-size effects.

Original languageEnglish (US)
Pages (from-to)8343-8352
Number of pages10
JournalPhysical Review B
Issue number16
StatePublished - 1987
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics


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