Ground state of weakly repulsive soft-core bosons on a sphere

Abstract

We study a system of penetrable bosons embedded in a spherical surface. Under the assumption of weak interaction between the particles, the ground state of the system is, to a good approximation, a pure condensate. We employ thermodynamic arguments to investigate, within a variational ansatz for the single-particle state, the crossover between distinct finite-size "phases" in the parameter space spanned by the sphere radius and the chemical potential. In particular, for radii up to a few interaction ranges we examine the stability of the fluid phase with respect to a number of crystal-like arrangements having the symmetry of a regular or semi-regular polyhedron. We find that, while quantum fluctuations keep the system fluid at low density, upon compression it eventually becomes inhomogeneous, i.e., particles gather together in clusters. As the radius increases, the nature of the high-density aggregate varies and we observe a sequence of transitions between different cluster phases ("solids"), whose underlying rationale is to maximize the coordination number of clusters, while ensuring at the same time the proper distance between each neighboring pair. We argue that, at least within our mean-field description, every cluster phase is supersolid.

38 pages, 12 figures

References in corpus (12)

• Supersolid formation in a quantum gas breaking continuous translational symmetry
• Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential
• Supersolid hardcore bosons on the triangular lattice
• A superfluid-droplet crystal and a free-space supersolid in a dipole-blockaded gas
• Atom trapping and two-dimensional Bose-Einstein condensates in field-induced adiabatic potentials
• Mean-field and stability analysis of two-dimensional flowing soft-core bosons modeling a supersolid
• Diffusion and Relaxation Dynamics in Cluster Crystals
• Ground state of two electrons on a sphere
• Nonclassical rotational inertia for a supersolid under rotation
• A fingerprint of surface-tension anisotropy in the free-energy cost of nucleation
• The structure of colloidosomes with tunable particle density: simulation vs experiment
• Cluster phases of penetrable rods on a line

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• Ultracold Bosons on a Regular Spherical Mesh
• Classical and Quantum Gases on a Semiregular Mesh
• Entropy Multiparticle Correlation Expansion for a Crystal