Superglass Phase of ${}^4\mathrm{He}$

We study different solid phases of ${}^4\mathrm{He}$, by means of path integral Monte Carlo simulations based on a recently developed worm algorithm. Our study includes simulations that start off from a high-$T$ gas phase, which is then “quenched” down to $T=0.2\mathrm{K}$. The low-$T$ properties of the system crucially depend on the initial state. While an ideal hcp crystal is a clear-cut insulator, the disordered system freezes into a superglass, i.e., a metastable amorphous solid featuring off-diagonal long-range order and superfluidity.

Figure 1

Pair correlation function of the ideal ${}^4\mathrm{He}$ hcp solid and superglass at the near-melting ($n=0.0292{\AA }^{-3}$, lower panel) and higher ($n=0.0359{\AA }^{-3}$, upper panel) densities.

Figure 2

Single-particle density matrix $n(r)$ for ideal ${}^4\mathrm{He}$ hcp crystal (filled symbols) and superglass (open symbols) at the near-melting density $n=0.0292{\AA }^{-3}$ (squares) and high-density $n=0.0359{\AA }^{-3}$ (circles). Solid lines through filled symbols represent exponential decay.

Figure 3

Condensate wave function at $n=0.0359{\AA }^{-3}$ (represented by the density of points) and $T=0.2\mathrm{K}$, obtained by making ten slices of the system along the $\widehat{z}$ direction and projecting them on the $xy$ plane (slices are ordered from left bottom to left top and then from right bottom to right top).