Curved geometry and Graphs

Abstract

Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a particle hopping on the graph. We discuss the role of connectivity in emergent Lorentzian perturbations in a curved background and the Bose-Hubbard (BH) model defined on graphs with particular symmetries. © Published under licence by IOP Publishing Ltd.