Microscopic characterization of overpressurized superfluid4He

We have studied static and dynamical properties of superfluid ${}^{4}$He at $T=0$ K in the pressure range from $\ensuremath{-}6$ up to 87 atm well above freezing into the metastable region. Zero temperature properties have been obtained with the exact shadow path integral ground state (SPIGS) method. Information about dynamic structure factors at different pressures have been obtained from imaginary time correlation functions via the genetic inversion via falsification of theories (GIFT) method. In the full pressure range sharp roton excitations are always present in the spectral functions. The roton energy decreases at higher pressures in good agreement with experimental data also in the metastable region. The roton energies have essentially a linear trend with pressure, going from about 7.4 K near freezing to about 4.3 K at about 87 atm. The pressure at which the linear trend would extrapolate to a zero roton energy turns out to be about 170 atm. At $T=0$ K, no sign of metastable glass phase has been found; the disordered systems studied at pressures above about 87 atm readily start homogeneous nucleation processes. Our results in the metastable phase for the condensate fractions and roton gaps differ remarkably from previous ones obtained via a diffusion Monte Carlo study.