A variational mean-field study of clusterization in a zero-temperature system of soft-core bosons

Abstract

We work out the ground-state diagram of weakly-repulsive penetrable bosons, using mean-field theory with a Gaussian ansatz on the single-particle wave function. Upon compression, the fluid transforms into a cluster supersolid, whose structure is characterized for various choices of the embedding space. In Euclidean space, the stable crystals are those with the most compact structure, i.e., triangular and fcc in two and three dimensions, respectively. For particles confined in a spherical surface, as the sphere radius increases we observe a sequence of transitions between different cluster phases, all having a regular or semiregular polyhedron as supporting frame for the clusters. The present results are relevant for the behavior of ultracold bosons weakly coupled to a Rydberg state.

Ultracold Bosons on a Regular Spherical Mesh

“…into regular polyhedral structures, that are simply unknown to Euclidean space—see Refs. [ 39 , 40 , 41 ]. An added value of a spherical mesh of points is the possibility to vary the site coordination while keeping the overall geometry strictly two-dimensional.…”

Bose-Hubbard model on polyhedral graphs

“…Our interest goes to regular or semiregular polyhedra inscribed in a sphere, since these ensure sufficient homogeneity in the coordination of vertices, a property shared with lattices. The use of spherical boundary conditions (SBC) has often been exploited in the past to discourage long-range ordering at high density [16][17][18][19][20][21][22][23][24].…”