Quantum Graphity: a model of emergent locality

TL;DR

Quantum graphity is a background independent model demonstrating how locality, geometry, and matter can emerge from dynamical graphs, with a stable low-energy phase exhibiting ordered, local structures and emergent gauge theories.

Contribution

The paper introduces a novel background independent model for emergent locality and geometry, showing a low-energy ordered phase and emergent gauge fields, with reformulation in graph-theoretic terms.

Findings

High-energy state is highly connected and symmetric.

Low-energy state breaks permutation symmetry and is ordered and local.

Emergent U(1) gauge theory arises via string-net condensation.

Abstract

Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly connected and the physics is invariant under the full symmetric group acting on the vertices. We present evidence that the model also has a low-energy phase in which the graph describing the system breaks permutation symmetry and appears to be ordered, low-dimensional and local. Consideration of the free energy associated with the dominant terms in the dynamics shows that this low-energy state is thermodynamically stable under local perturbations. The model can also give rise to an emergent U(1) gauge theory in the ground state by the string-net condensation mechanism of Levin and Wen. We also reformulate the model in graph-theoretic terms and compare its dynamics to some common graph processes.