Quantum graphity: A model of emergent locality

Tomasz Konopka, Fotini Markopoulou, and Simone Severini
Phys. Rev. D 77, 104029 – Published 27 May 2008

Abstract

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.

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  • Received 30 January 2008

DOI:https://doi.org/10.1103/PhysRevD.77.104029

©2008 American Physical Society

Authors & Affiliations

Tomasz Konopka1, Fotini Markopoulou2,3, and Simone Severini3

  • 1ITP, Utrecht University, Utrecht 3584 CE, The Netherlands
  • 2Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 Canada
  • 3University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

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Issue

Vol. 77, Iss. 10 — 15 May 2008

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