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Background independent condensed matter models for quantum gravity
General Relativity and Quantum Cosmology · Submitted 26 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This model has primitive notions of gravitational attraction which we illustrate with a toy black hole, and exhibits entanglement between matter and geometry and thermalization of the quantum geometry.
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The abstract, sentence by sentence
A number of recent proposals for 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 fundamental challenges to any such approach. At the conceptual level, there is a clash between the "timelessness" of general relativity and emergence. Second, the lack of a fundamental spacetime makes difficult the straightforward application of well-known methods of statistical physics to the problem. We recently initiated a study of such problems using spin systems based on evolution of quantum networks with no a priori geometric notions as models for emergent geometry and gravity. In this article we review two such models. The first is a model of emergent (flat) space and matter and we show how to use methods from quantum information theory to derive features such as speed of light from a non-geometric quantum system. The second model exhibits interacting matter and geometry, with the geometry defined by the behavior of matter. This model has primitive notions of gravitational attraction which we illustrate with a toy black hole, and exhibits entanglement between matter and geometry and thermalization of the quantum geometry.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A number of recent proposals for 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. | background 1.00 | 0.04 | 0.03 | asserted 0.99 |
| s1 | There are two fundamental challenges to any such approach. | background 0.93 | 0.06 | 0.02 | asserted 0.98 |
| s2 | At the conceptual level, there is a clash between the "timelessness" of general relativity and emergence. | background 0.97 | 0.05 | 0.02 | asserted 1.00 |
| s3 | Second, the lack of a fundamental spacetime makes difficult the straightforward application of well-known methods of statistical physics to the problem. | background 0.94 | 0.04 | 0.02 | asserted 0.98 |
| s4 | We recently initiated a study of such problems using spin systems based on evolution of quantum networks with no a priori geometric notions as models for emergent geometry and gravity. | contribution 0.81 | 0.90 | 0.06 | asserted 0.99 |
| s5 | In this article we review two such models. | contribution 0.97 | 0.47 | 0.04 | asserted 0.90 |
| s6 | The first is a model of emergent (flat) space and matter and we show how to use methods from quantum information theory to derive features such as speed of light from a non-geometric quantum system. | contribution 0.77 | 0.92 | 0.19 | asserted 1.00 |
| s7 | The second model exhibits interacting matter and geometry, with the geometry defined by the behavior of matter. | contribution 0.78 | 0.78 | 0.11 | asserted 1.00 |
| s8 | This model has primitive notions of gravitational attraction which we illustrate with a toy black hole, and exhibits entanglement between matter and geometry and thermalization of the quantum geometry. | result 0.82 | 0.86 | 0.16 | asserted 1.00 |
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The paper
Original abstract
A number of recent proposals for 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 fundamental challenges to any such approach. At the conceptual level, there is a clash between the "timelessness" of general relativity and emergence. Second, the lack of a fundamental spacetime makes difficult the straightforward application of well-known methods of statistical physics to the problem. We recently initiated a study of such problems using spin systems based on evolution of quantum networks with no a priori geometric notions as models for emergent geometry and gravity. In this article we review two such models. The first is a model of emergent (flat) space and matter and we show how to use methods from quantum information theory to derive features such as speed of light from a non-geometric quantum system. The second model exhibits interacting matter and geometry, with the geometry defined by the behavior of matter. This model has primitive notions of gravitational attraction which we illustrate with a toy black hole, and exhibits entanglement between matter and geometry and thermalization of the quantum geometry.
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References
How the literature uses it
12 arXiv papers cite this in 15 sentences
Papers citing it · 9 sentences without a confident label
Compares with it 1 paper
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Our approach is different from the standard one, studied in the perturbative framework: instead of “for all practical purposes” inevitable fast interaction-induced decoherence from initially product states between two sub-systems [ref] , we show that the gauge symmetry requirements (coming in particular from the local Poincaré symmetry) secure the entangled states between matter and gravity as physical states.
Gauge protected entanglement between gravity and matter · Introduction · 0.85
Cites it as background 5 papers
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For this reason, phenomenological approaches have become some of the main tools to tackle the problem of QG [ref] (see [ref] for a recent review).
Dark Matter as an effect of a minimal length · Introduction · 0.82
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Potential QG signatures in condensed matter, atomic and molecular experiments have been explored by various authors [ref] .
Test of Quantum Gravity in Statistical Mechanics · Introduction · 0.90
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A lot of significant phenomenological work has been done so far [ref] .
Baryon Asymmetry from the Generalized Uncertainty Principle · Introduction · 0.86
What it cites · 29 sentences without a confident label
Builds on 3 papers
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To extend this construction to the case in which the ${ j_ij }$ degrees of freedom are not frozen in a particular lattice $Γ_N$ like the square lattice of Fig.[ref](a-b), in [ref] we modified the Hamiltonian of [ref] to the terms: H_loops =-g_L∑_loops∑_L=0^∞r^L/L! ∏_a=1^L M_a^±,
Quantum Graphity · Quantum graphity: A model of emergent geometry and matter · 1.00
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To extend this construction to the case in which the ${ j_ij }$ degrees of freedom are not frozen in a particular lattice $Γ_N$ like the square lattice of Fig.[ref](a-b), in [ref] we modified the Hamiltonian of [ref] to the terms: H_loops =-g_L∑_loops∑_L=0^∞r^L/L! ∏_a=1^L M_a^±,
A lattice bosonic model as a quantum theory of gravity · Quantum graphity: A model of emergent geometry and matter · 1.00
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This exchange is done using the term in the Hamiltonian[ In [ref] , we introduced the more general Hamiltonian that created $R$ pairs of bosons for every link destroyed, and vice versa: H_ex=k∑_ij(|0⟩⟨1|_ij(b^†_i b^†_j)^R+ |1⟩⟨0|_ij( b_ib_j)^R).
A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime · A unitary model of interacting matter and geometry · 0.88
Uses the method or tool of 1 paper
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This can be done by mapping $K_N$ to its line graph $L(K_N)$, as follows [ref] : Every edge of $K_N$ maps to a vertex in $L(K_N)$.
Properties of Quantum Graphity at Low Temperature · From a dynamical to a fixed lattice · 0.93
Cites as background 13 papers
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Quantum graphity, first proposed in [ref] and [ref] , is a spin system in which locality, geometric symmetries, and matter arise at low energy, when a spin system is cooled to its ground state.
Quantum Graphity · Quantum graphity: A model of emergent geometry and matter · 0.96
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We will now review the two models of [ref] and [ref] .
A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime · Purpose of models. · 0.94
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Wen's work on emergent matter and gravitons from a bosonic spin system [ref] , the broader idea of spacetime as a condensate [ref] , or aspects of emergence in Causal Dynamical Triangulations [ref] and Group Field Theory, and similar ideas in a simplicial [ref] and causal models [ref] .
The Self-Organized de Sitter Universe · Introduction · 0.97
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