Spinfoam on a Lefschetz thimble: Markov chain Monte Carlo computation of a Lorentzian spinfoam propagator

Han, Muxin; Huang, Zichang; Liu, Hongguang; Qu, Dongxue; Wan, Yidun

doi:10.1103/physrevd.103.084026

Cited by 38 publications

(30 citation statements)

References 64 publications

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“…For example, the spectral dimension of cuboid spin foams is solely determined by the scaling behavior of the amplitude, which we thus expect to change at small spins. We hope that similar calculations become possible soon for the full model defined on triangulations thanks to the development of powerful numerical tools [12,25,27] as well as using effective spin foam models [34,36,37] and Lefshetz-thimble Monte Carlo techniques [38].…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…to explore the so-called "flatness problem" in spin foams [30][31][32][33][34][35], yet they remain challenging due to rapidly growing numerical costs as the representation labels are increased. Additionally, these promising results are complemented by developments that will help to unlock larger 2-complexes: effective spin foam models [34,36,37] bypass this numerical challenge by directly starting from the asymptotic formula to investigate under which conditions reasonable semi-classical physics emerge, while Lefshetz thimbles enable the use of Monte Carlo methods to compute expectation values of observables on larger 2-complexes [38].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical evaluation of spin foam amplitudes beyond simplices

Allen,

Girelli,

Steinhaus

2022

Preprint

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We present the first numerical calculation of the 4D Euclidean spin foam vertex amplitude for vertices with hypercubic combinatorics. Concretely, we compute the amplitude for coherent boundary data peaked on cuboid and frustum shapes. We present the numerical algorithms to explicitly compute the vertex amplitude and compare the results in different cases to the semi-classical approximation of the amplitude. Overall we find good qualitative agreement of the amplitudes and evidence of convergence of the asymptotic formula to the full amplitude already at fairly small spins, yet also differences in the frequency of oscillations and a phase shift absent in the 4-simplex case. However, due to rapidly growing numerical costs, we cannot reach sufficiently high spins to prove agreement of both amplitudes. Lastly, this setup allows us to explore non-uniform vertex amplitudes, where some representations are small while others are large; we find indications that scenarios might exist in which the semi-classical amplitude is a valid approximation even if some spins remain small. This suggests that the transition of the quantum to the semi-classical regime (for a single vertex amplitude) is intricate.

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Section: Discussion and Outlookmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical evaluation of spin foam amplitudes beyond simplices

Allen,

Girelli,

Steinhaus

2022

Preprint

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“…There are a few other future aspects that we would like to mention: Recently various numerical techniques have been applied to the EPRL spinfoam model with spacelike tetrahedra [29,30]. It is interesting to generalize these numerical methods to include the extended model with timelike tetrahedra/polyhedra, see [31] for the first step.…”

Section: Discussionmentioning

confidence: 99%

Finiteness of spinfoam vertex amplitude with timelike polyhedra, and the full amplitude

Han,

Kaminski,

Liu

2021

Preprint

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This work focuses on Conrady-Hnybida's 4-dimensional extended spinfoam model with timelike polyhedra, while we restrict all faces to be spacelike. Firstly, we prove the absolute convergence of the vertex amplitude with timelike polyhedra, when SU(1,1) boundary states are coherent states or the canonical basis, or their finite linear combinations. Secondly, based on the finite vertex amplitude and a proper prescription of the SU(1,1) intertwiner space, we construct the extended spinfoam amplitude on arbitrary cellular complex, taking into account the sum over SU(1,1) intertwiners of internal timelike polyhedra. We observe that the sum over SU(1,1) intertwiners is infinite for the internal timelike polyhedron that has at least 2 future-pointing and 2 past-pointing face-normals. In order to regularize the possible divergence from summing over SU(1,1) intertwiners, we develop a quantum cut-off scheme based on the eigenvalue of the "shadow operator". The spinfoam amplitude with timelike internal polyhedra (and spacelike faces) is finite, when 2 types of cut-offs are imposed: one is imposed on j the eigenvalue of area operator, the other is imposed on the eigenvalue of shadow operator for every internal timelike polyhedron that has at least 2 future-pointing and 2 past-pointing face-normals.

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“…With the term 'propagator' werefer to the square matrices (they are such since the self-energy triangulation has two boundarytetrahedra) in which the element a, b corresponds to the amplitude ( 13) with a = i + , b = i − . Computing the expectation values (A4) of geometric operators describing boundary tetrahedra is a significant numerical investigation, especially considering that computations carried out with the EPRL model are still in their primordial stages [44,[51][52][53][54][55], and, as far as we know, at present time there are no such numerical computations with spinfoams containing a bubble. Since in the calculation of (A4) the dimensional factor of the boundary intertwiners is relevant, in this section it is convenient to define a 'normalized' amplitude as:…”

Section: Boundary Observablesmentioning

confidence: 99%

Numerical analysis of the self-energy in covariant Loop Quantum Gravity

Frisoni,

Gozzini,

Vidotto

2021

Preprint

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We study numerically the first order radiative corrections to the self-energy, in covariant loop quantum gravity. We employ the recently developed sl2cfoam-next spinfoam amplitudes library, and some original numerical methods. We analyze the scaling of the divergence with the infrared cutoff, for which previous analytical estimates provided widely different lower and upper bounds. Our findings suggest that the divergence is approximately linear in the cutoff. We also investigate the role of the Barbero-Immirzi parameter in the asymptotic behavior, the dependence of the scaling on some boundary data and the expectation values of boundary operators.

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Spinfoam on a Lefschetz thimble: Markov chain Monte Carlo computation of a Lorentzian spinfoam propagator

Cited by 38 publications

References 64 publications

Numerical evaluation of spin foam amplitudes beyond simplices

Numerical evaluation of spin foam amplitudes beyond simplices

Finiteness of spinfoam vertex amplitude with timelike polyhedra, and the full amplitude

Numerical analysis of the self-energy in covariant Loop Quantum Gravity

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