Quantum graphity: A model of emergent locality

@article{Konopka2008QuantumGA,
  title={Quantum graphity: A model of emergent locality},
  author={Tomasz Konopka and Fotini Markopoulou and Simone Severini},
  journal={Physical Review D},
  year={2008},
  volume={77},
  pages={104029}
}
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… 
View PDF on arXiv
156 Citations
Highly Influential Citations
2
Background Citations
56
Methods Citations
10
Results Citations
3

Figures and Tables from this paper

156 Citations

Properties of quantum graphity at low temperature

We present a mapping of dynamical graphs and, in particular, the graphs used in the Quantum Graphity models for emergent geometry, to an Ising Hamiltonian on the line graph of a complete graph with a…

Quantum bose-hubbard model with an evolving graph as a toy model for emergent spacetime

We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric…

The Structurally Dynamic Cellular Network and Quantum Graphity Approaches to Quantum Gravity - A Review and Comparison

Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to…

The Structurally Dynamic Cellular Network and Quantum Graphity Approaches to Quantum Gravity and Quantum Geometry - A Review and Comparison

This paper views continuum concepts and continuum spacetime in particular as being emergent, coarse-grained and derived relative to this underlying erratic and disordered microscopic substratum, which it would like to call quantum geometry and which is expected to play by quite different rules, namely generalized cellular automaton rules.

Geometric Graphity and the Gravitization of Quantum Mechanics

We propose and prove three theorems in an axiomatic extension of Quantum Mechanics to a noncommutative spacetime geometry. The geometry is built from the Clifford Algebras Cl(R3) and Cl(R2), where…

Nonlocal and Light Cone Dynamics Emergent from Information-Propagating Complete Graph

It is argued that this superluminal velocity corresponds to the quantum mechanical discontinuous motion of particles and provides possibilities for descriptions of entanglement and particle spin within the system and makes this system nontrivial and worthy of further investigation.

Random holographic "large worlds" with emergent dimensions.

A random network model governed by a Gaussian weight corresponding to Ising link antiferromagnetism as a model for emergent quantum space-time, where the quenched graphs constitute a discrete version of a 5D-space-filling surface with a number of fundamental degrees of freedom scaling like N^{2/5}, a graph version of the holographic principle.

Domain structures in quantum graphity

Quantum graphity offers the intriguing notion that space emerges in the low-energy states of the spatial degrees of freedom of a dynamical lattice. Here we investigate metastable domain structures…

A model of quantum gravity with emergent spacetime

We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal…

Background-independent condensed matter models for quantum gravity

A number of recent proposals on a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two…
...

References

SHOWING 1-10 OF 77 REFERENCES

Quantum Graphity

We introduce a new model of background independent physics in which the degrees of freedom live on a complete graph and the physics is invariant under the permutations of all the points. We argue…

String-net condensation: A physical mechanism for topological phases

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called ``string-nets,''…

Scale Free Small World Networks and the Structure of Quantum Space-Time

We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain…

2D Ising Model with non-local links - a study of non-locality

Markopoulou and Smolin have argued that the low energy limit of LQG may suffer from a conflict between locality, as defined by the connectivity of spin networks, and an averaged notion of locality…

Quantum) spacetime as a statistical geometry of lumps in random networks

In the following we undertake to describe how macroscopic spacetime (or rather, a microscopic protoform of it) is supposed to emerge as a superstructure of a web of lumps in a stochastic discrete…

Quantum Gravity, or The Art of Building Spacetime

The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological…

Fermions, strings, and gauge fields in lattice spin models

We investigate the general properties of lattice spin models with emerging fermionic excitations. We argue that fermions always come in pairs and their creation operator always has a stringlike…

TASI Lectures on Matrix Theory

This is a summary of key issues in Matrix Theory and its compactifications. It is emphasized that Matrix Theory is a valid Discrete Light Cone Quantization of M Theory with at least 6 noncompact…

Group field theory as the microscopic description of the quantum spacetime fluid: a new perspective on the continuum in quantum gravity

We introduce the group field theory (GFT) formalism for non-perturbative quantum gravity, and present it as a potential unifying framework for several other quantum gravity approaches, i.e. loop…

Background independent quantum gravity: A Status report

The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum…
...