A Monte Carlo algorithm for spin foam intertwiners
arXiv:2403.04836 · doi:10.1103/PhysRevD.110.026022
Abstract
Monte Carlo algorithms are barely considered in spin foam quantum gravity. Due to the quantum nature of spin foam amplitudes one cannot readily apply them, and the present sign problem is a threat to convergence and thus efficiency. Yet, ultimately the severity of the sign problem in spin foams is not known. In this article we propose a new probability distribution for coherent (boundary) intertwiners, which we use to define a Markov Chain Monte Carlo algorithm. We apply this algorithm to the SU(2) coherent vertex amplitude for various Regge-type boundary data and find convergent, accurate results at far lower costs than the explicit calculation. The resources are instead used to increase the size of boundary spins, bridging the gap to the asymptotic formulae. While the sign problem is not solved, it is under control in the vast majority of cases. We close by discussing how this algorithm can be extended to larger triangulations with boundary and 4d Lorentzian spin foam models. More speculatively, we discuss how this algorithm can be used to sample (Regge-geometric) bulk intertwiners.
42 pages, 15 figures; v2: matching version accepted for publication in PRD, expanded on explanation of algorithm, added appendix describing convergence properties of algorithm for different boundary data
References in corpus (63)
- Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
- The Spin Foam Approach to Quantum Gravity
- Tensor renormalization group approach to 2D classical lattice models
- LQG vertex with finite Immirzi parameter
- A new spinfoam vertex for quantum gravity
- Nonperturbative Quantum Gravity
- Tensor Network Renormalization
- A New Spin Foam Model for 4d Gravity
- Lorentzian spin foam amplitudes: graphical calculus and asymptotics
- Asymptotic analysis of the EPRL four-simplex amplitude
- The causal set approach to quantum gravity
- On the semiclassical limit of 4d spin foam models
- Area-angle variables for general relativity
- Coarse graining methods for spin net and spin foam models
- Decorated tensor network renormalization for lattice gauge theories and spin foam models
- Numerical evidence for a phase transition in 4d spin foam quantum gravity
- Fusion basis for lattice gauge theory and loop quantum gravity
- Effective Spin Foam Models for Four-Dimensional Quantum Gravity
- Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
- Towards a phase diagram for spin foams
- Hypercuboidal renormalization in spin foam quantum gravity
- SU(2) graph invariants, Regge actions and polytopes
- Investigation of the Spinfoam Path integral with Quantum Cuboid Intertwiners
- Quantum gravity asymptotics from the SU(2) 15j symbol
- Holonomy spin foam models: Asymptotic geometry of the partition function
- Coarse graining flow of spin foam intertwiners
- Coarse graining of spin net models: dynamics of intertwiners
- Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity
- Boosting Wigner's nj-symbols
- Quantum group spin nets: refinement limit and relation to spin foams
- Quantum gravity kinematics from extended TQFTs
- Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
- Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
- Discrete gravity dynamics from effective spin foams
- Asymptotic analysis of spin foam amplitude with timelike triangles
- Numerical analysis of spin foam dynamics and the flatness problem
- Asymptotic analysis of the EPRL model with timelike tetrahedra
- The Cuba Library
- Towards a Cosmological subsector of Spin Foam Quantum Gravity
- Computing the renormalization group flow of two-dimensional theory with tensor networks
- How-To compute EPRL spin foam amplitudes
- Path integral suppression of badly behaved causal sets
- From spin foams to area metric dynamics to gravitons
- Emergence of Spacetime in a restricted Spin-foam model
- 2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions
- Asymptotic analysis of spin-foams with time-like faces in a new parameterisation
- Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double- complex
- Regge calculus models of the closed vacuum -FLRW universe
- Spin-foams as semi-classical vertices: gluing constraints and a hybrid algorithm
- Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
- Summing bulk quantum numbers with Monte Carlo in spin foam theories
- Tensor network approach to 2d Lorentzian quantum Regge calculus
- Radiative corrections to the Lorentzian EPRL spin foam propagator
- Numerical evaluation of spin foam amplitudes beyond simplices
- Hopf link volume simplicity constraints in spin foam models
- The accidental flatness constraint does not mean a wrong classical limit
- Spinfoams: Foundations
- Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
- Numerical approach to the black-to-white hole transition
- Toward matter dynamics in spin foam quantum gravity
- Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics
- Curvature effects in the spectral dimension of spin foams
- A Wick rotation for EPRL spin foam models