TL;DR
This paper explores how curved geometries and Lorentzian perturbations emerge from quantum graph models, focusing on particle dynamics and the Bose-Hubbard model on symmetric graphs.
Contribution
It provides new insights into emergent geometry and Lorentzian perturbations within quantum graphity, emphasizing the role of connectivity and symmetry in these phenomena.
Findings
Connectivity influences emergent Lorentzian perturbations
Symmetric graphs facilitate the Bose-Hubbard model analysis
Emergent geometry is linked to particle hopping dynamics
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.
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