Off Diagonal Long Range Order in Low Temperature Solid Helium

Experiments have recently produced evidence of the existence of a supersolid $^{4}He$. One of the important properties of equilibrium superfluid/supersolid behavior is the existence of off diagonal long range order, defined in terms of the 1-body density matrix as $\lim_{\left|r-r'\right|\rightarrow\infty}\rho\left(r,r'\right)>0$ . Using path integral monte carlo, we calculate the off diagonal density matrix for solid $^{4}He$ at temperatures near the experiment and find it is very small at large $r$.