The Bose-Hubbard model on a flat-band lattice: A community of bosons

摘要

The Bose-Hubbard model is explored in a flat-band lattice by following the story of a community of bosons, whose movement is enforced by the mayor through taxes and earnings to illustrate the role of the tunnelling and the onsite interaction parameters. This model is then illustrated for a 1-D diamond lattice and the effect on the community is examined in order to explain the phase-type and the phase transition point. The model is frustrated, which is illustrated by having thieves along certain routes, meaning bosons can only get past by travelling in pairs. Additionally, the minimisation of the mayor's expenditure provides a parallel for obtaining the ground state energy of the model.