The Shadow Path Integral Ground State Method: Study of Confined Solid 4He

We have studied the zero temperature phase diagram of confined He-4 by means of a new exact projector Quantum Monte Carlo method: the Shadow Path Integral Ground State (SPIGS). This method is able to compute exact ground state expectation values without extrapolations and with a Shadow Wave Function (SWF) as trial variational state for the importance sampling. Thanks to the ability of SWF in describing the solid phase via spontaneously broken translational symmetry, this is an important extension which opens the possibility to study disorder phenomena in the solid phase by an exact method at zero temperature. We have applied this technique to study He-4 confined in a lattice of big static objects with a purely repulsive interaction with He-4 atoms. We have studied the equation of state of this system finding that a well defined liquid-solid transition is still present but with an increased freezing pressure. In the case we have studied this pressure goes from 25.2 atm for pure bulk system to about 38 atm. This is similar to what is experimentally found in He-4 confined in porous material like vycor. We have found also that the disorder due to the mismatch between the crystal structure and the spherical geometry of the object induces delocalization of He-4 atoms.