Shadow wave function for liquid and solidHe3

Abstract

The ideas of the shadow wave function are applied to construct a variational wave function to describe the liquid and the solid phase of a system that obeys Fermi statistics. The shadow variables are introduced in the symmetric correlating factor. The antisymmetric part is a standard determinant of plane waves modified by backflow effect. Variational Monte Carlo calculations for 3 He provide ground-state energies in the liquid phase at the level of the most elaborate trial function available in the literature. With this wave function, properties like translational invariance and antisymmetry under particle interchange are maintained even in the crystalline phase.

Iterative backflow renormalization procedure for many-body ground-state wave functions of strongly interacting normal Fermi liquids

“…Since the nodal surfaces of the exact ground state wavefunction are in general unknown, the energies of FN calculations do not converge to the exact ground state energy but remain above them by an unknown amount. Although methods which do not rely on the FN approximation have been developed [2][3][4][5][6] , they are in general limited to small systems as their computational cost grows exponentially with system size. Therefore, FN-QMC calculations still provide the most accurate values of ground state properties of extended fermion systems.…”

Analytical and Numerical (Monte Carlo) Studies of Point and Space Group Symmetry-Breaking in the Liquid–Solid Phase Transition

“…(43). Exploiting now relations (24) and (25) and inserting definition (9) of the two-body density in Eq. (120), one ultimately winds up with …”

“…In ongoing research we are employing group-theoretical tools developed in this work in (1) a variational shadow wave functions [24,25] Monte Carlo study of spontaneous crystallization of superfluid 4 He at zero temperature and in (2) a correlated wave functions treatment of solidification of superfluid 4 He [26]. The formal group-theoretical treatment of (x) and ρ 2 (x 1 , x 2 ) presented here might turn out to be useful in particular for electronic energy band structure calculations [7], for research on liquid crystals [8,15], and for the physics of adsorbed liquid and solid films.…”

On fermionic shadow wave functions for strongly correlated multi-reference systems based on a single Slater determinant

“…where det(φ α (r ↑ β )) and det(φ α (r ↓ β )) are SDs as a function of the electronic coordinates only [17]. Even though the ASWF already includes many-body correlation effects of any order, the FSWF is superior since it accounts not only for symmetric, but moreover also for asymmetric, threebody and backflow correlation effects [34,35].…”

“…In the present work we demonstrate that extending the Shadow Wave Function (SWF), which was first introduced by Kalos and coworkers [14,15], to fermionic systems allows bypass the static correlation problem and permits to study strongly-correlated multi-reference systems within a much more efficient single-determinant scheme [16][17][18][19][20].…”