2008/01/31 by Tomasz Konopka, Fotini Markopoulou, Simone Severini · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Graph #Graph theory #Ground state #Invariant (physics) #Locality #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Statistical physics #Theoretical physics #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.77.104029
published as Phys.Rev.D77:104029,2008 · 25 pages
arxiv created 2008/05/23 · openalex publication_date 2008/05/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quantum graphity is a background-independent model for emergent macroscopic 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.