Ultracold Bosons on a Regular Spherical Mesh

TL;DR

This paper investigates the zero-temperature phases of hard-core bosons on a spherical mesh using mean-field and numerical methods, revealing various quantum states including superfluid, solid, and supersolid phases.

Contribution

It introduces a study of bosonic particles on a spherical mesh with an extended Bose-Hubbard model, analyzing phase behavior with mean-field and numerical approaches.

Findings

Identification of gas, solid, supersolid, and superfluid phases.

Comparison of mean-field results with numerical diagonalization.

Signatures of spatial orders in finite quantum systems.

Abstract

I study the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh ("Platonic mesh") and interacting through an extended Bose-Hubbard Hamiltonian. Only the hard-core version of the model is considered here, for two instances of Platonic mesh. Using the mean-field decoupling approximation, I show that the system may exist in various ground states, which can be regarded as analogs of gas, solid, supersolid, and superfluid. For one mesh, by comparing the theoretical results with the outcome of numerical diagonalization, I manage to uncover the signatures of diagonal and off-diagonal spatial orders in a finite quantum system.