Cosmological Constant from Condensation of Defect Excitations

Dittrich, Bianca

doi:10.3390/universe4070081

Cited by 10 publications

(19 citation statements)

References 148 publications

(287 reference statements)

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“…Here we will only briefly sketch the main features of the fusion basis, which arises in anyon systems [97,98], (2+1)D lattice gauge theories [99] and 3D quantum gravity [100,101]. The algebraic structures are called Drinfeld Doubles, see [99,100,[102][103][104][105] for more details.…”

Section: Decorated Tensor Network For Lattice Gauge Theories and Spimentioning

confidence: 99%

Coarse Graining Spin Foam Quantum Gravity—A Review

Steinhaus

2020

Front. Phys.

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Section: Decorated Tensor Network For Lattice Gauge Theories and Spimentioning

confidence: 99%

Coarse Graining Spin Foam Quantum Gravity—A Review

Steinhaus

2020

Front. Phys.

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“…The fusion basis arises in (2 + 1)-dimensional anyon systems [41,42], but it can be also constructed for (2 + 1)-dimensional lattice gauge theories [26], as well as for (2 + 1)-dimensional gravity [12,25]. The associated algebraic structures, the so-called Drinfeld Doubles, have been discussed for various physics applications [25,26,[43][44][45][46].…”

Section: Fusion Basis In a Nutshellmentioning

confidence: 99%

“…We first transform the tree for the gluing building block (12) into a new tree, so that the puncture pairs (2, 2 ) and (4, 4 ), which lay on opposite faces, can be coarse-grained. The necessary transformations are split into several steps as depicted in Figures 5-8.…”

Section: Fusion Basis Transformationsmentioning

confidence: 99%

“…In this work we present a tensor network renormalization algorithm applicable to three-dimensional lattice gauge systems, three-dimensional quantum gravity models [12], as well as the study of anyon condensation.…”

Section: Introductionmentioning

confidence: 99%

“…As k increases, the cosmological constant decreases. The question is whether one can define an effective theory that corresponds to a cosmological constant larger than the one specified by the level k, as well as study transitions between these theories [12]. The idea is that such an effective theory would arise as a "condensation" of curvature defects (with respect the vacuum at level k).…”

Section: Introductionmentioning

confidence: 99%

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Tensor Network Renormalization with Fusion Charges—Applications to 3D Lattice Gauge Theory

2020

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Tensor network methods are powerful and efficient tools for studying the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods have been applied to lattice gauge theories, yet these theories remain a challenge in ( 2 + 1 ) dimensions. In this article, we present a new (decorated) tensor network algorithm, in which the tensors encode the lattice gauge amplitude expressed in the fusion basis. This has several advantages—firstly, the fusion basis does diagonalize operators measuring the magnetic fluxes and electric charges associated to a hierarchical set of regions. The algorithm allows therefore a direct access to these observables. Secondly the fusion basis is, as opposed to the previously employed spin network basis, stable under coarse-graining. Thirdly, due to the hierarchical structure of the fusion basis, the algorithm does implement predefined disentanglers. We apply this new algorithm to lattice gauge theories defined for the quantum group SU ( 2 ) k and identify a weak and a strong coupling phase for various levels k . As we increase the level k , the critical coupling g c decreases linearly, suggesting the absence of a deconfining phase for the continuous group SU ( 2 ) . Moreover, we illustrate the scaling behaviour of the Wilson loops in the two phases.

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q deformed formulation of Hamiltonian SU(3) Yang-Mills theory

Hayata,

Hidaka

2023

J. High Energ. Phys.

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We study SU(3) Yang-Mills theory in (2 + 1) dimensions based on networks of Wilson lines. With the help of the q deformation, networks respect the (discretized) SU(3) gauge symmetry as a quantum group, i.e., SU(3)k, and may enable implementations of SU(3) Yang-Mills theory in quantum and classical algorithms by referring to those of the stringnet model. As a demonstration, we perform a mean-field computation of the groundstate of SU(3)k Yang-Mills theory, which is in good agreement with the conventional Monte Carlo simulation by taking sufficiently large k. The variational ansatz of the mean-field computation can be represented by the tensor networks called infinite projected entangled pair states. The success of the mean-field computation indicates that the essential features of Yang-Mills theory are well described by tensor networks, so that they may be useful in numerical simulations of Yang-Mills theory.

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Cosmological Constant from Condensation of Defect Excitations

Cited by 10 publications

References 148 publications

Coarse Graining Spin Foam Quantum Gravity—A Review

Coarse Graining Spin Foam Quantum Gravity—A Review

Tensor Network Renormalization with Fusion Charges—Applications to 3D Lattice Gauge Theory

q deformed formulation of Hamiltonian SU(3) Yang-Mills theory

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