Estimation of the condensate fraction from the static structure factor

Abstract

We present an analytical method to estimate the condensate fraction $n_0/n$ in strongly correlated systems for which the zero-temperature static structure factor $S({\bf p})$ is known. The advantage of the proposed method is that it allows one to predict the long-range behavior of the one-body density matrix (i) in macroscopic and mesoscopic systems, (ii) in three- and two-dimensional geometry, (iii) at zero and low finite temperature, and (iv) in weakly and strongly correlated regimes. Our method is tested against exact values obtained with various quantum Monte Carlo methods in a number of strongly correlated systems showing an excellent agreement. The proposed technique is also useful in numerical simulations as it allows one to extrapolate the condensate fraction to the thermodynamic limit for particle numbers as small as tens to hundreds. Our method is especially valuable for extracting the condensate fraction from the experimentally measured static structure factor $S({\bf p})$, thus providing a new simple alternative technique for the estimation of $n_0/n$. We analyze available experimental data for $S({\bf p})$ of superfluid helium and find an excellent agreement with the experimental value of $n_0/n$.