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

Abstract

A study by Magro and Ceperley [Phys. Rev. Lett. 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 $\ensuremath{\rho}(r).$ 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. The algebraic decay of the one-body density matrix is due to correlations between phase fluctuations, and we find that the exponent in the power law 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.