Single-particle density matrix and superfluidity in the two-dimensional Bose Coulomb fluid

A study by W. R. Magro and D. M. Ceperley [Phys. Rev. Lett. {\bf 73}, 826 (1994)] has shown that the ground state of the two-dimensional fluid of charged bosons with logarithmic interactions is not Bose-condensed, but exhibits algebraic off-diagonal order in the single-particle density matrix $\rho(r)$. We use a hydrodynamic Hamiltonian expressed in terms of density and phase operators, in combination with an $f$-sum rule on the superfluid fraction, to reproduce these results and to extend the evaluation of the density matrix to finite temperature $T$. This approach allows us to treat the liquid as a superfluid in the absence of a condensate. We find that (i) the off-diagonal order arises from the correlations between phase fluctuations; and (ii) the exponent in the power-law decay of $\rho(r)$ is determined by the superfluid density $n_s(T)$. We also find that the plasmon gap in the single-particle energy spectrum at long wavelengths decreases with increasing $T$ and closes at the critical temperature for the onset of superfluidity.