Quantum group spin nets: refinement limit and relation to spin foams

Abstract

So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups $\text{SU}(2{)}_k$ and examine their effective continuum dynamics via tensor network renormalization. In the refinement limit of this coarse graining procedure, we find a vast non-trivial fixed point structure beyond the degenerate and the $BF$ phase. In comparison to previous work, we use fixed point intertwiners, inspired by Reisenberger's construction principle [1] and the recent work [2], as the initial parametrization. In this new parametrization fine tuning is not required in order to flow to these new fixed points. Encouragingly, each fixed point has an associated extended phase, which allows for the study of phase transitions in the future. Finally we also present an interpretation of spin nets in terms of melonic spin foams. The coarse graining flow of spin nets can thus be interpreted as describing the effective coupling between two spin foam vertices or space time atoms.

30+5 pages, many figures, v2: references added

References in corpus (16)

• Tensor renormalization group approach to 2D classical lattice models
• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Perfect discretization of reparametrization invariant path integrals
• Holonomy Spin Foam Models: Definition and Coarse Graining
• Operator Spin Foam Models
• Simulation of anyons with tensor network algorithms
• Coarse graining free theories with gauge symmetries: the linearized case
• Observables in Loop Quantum Gravity with a cosmological constant
• The area law and real-space renormalization
• On knottings in the physical Hilbert space of LQG as given by the EPRL model
• Topological lattice field theories from intertwiner dynamics
• q-Deformed spin foam models of quantum gravity
• Discretizing parametrized systems: the magic of Ditt-invariance

Cited by in corpus (31)

• Quantum Cosmology from Group Field Theory Condensates: a Review
• Decorated tensor network renormalization for lattice gauge theories and spin foam models
• Numerical evidence for a phase transition in 4d spin foam quantum gravity
• A new vacuum for Loop Quantum Gravity
• Effective Spin Foam Models for Lorentzian Quantum Gravity
• Towards a phase diagram for spin foams
• Hypercuboidal renormalization in spin foam quantum gravity
• Investigation of the Spinfoam Path integral with Quantum Cuboid Intertwiners
• Coarse graining flow of spin foam intertwiners
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
• Quantum gravity kinematics from extended TQFTs
• Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
• Discrete gravity dynamics from effective spin foams
• Discretization independence implies non-locality in 4D discrete quantum gravity
• Pachner moves in a 4d Riemannian holomorphic Spin Foam model
• Einstein Equation from Covariant Loop Quantum Gravity in Semiclassical Continuum Limit
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
• An elementary introduction to loop quantum gravity
• Towards a Cosmological subsector of Spin Foam Quantum Gravity
• Quantization of systems with temporally varying discretization II: Local evolution moves
• Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces
• From 3D topological quantum field theories to 4D models with defects
• Quantum Gravity on the computer: Impressions of a workshop
• Visions in Quantum Gravity
• Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• A new realization of quantum geometry
• Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
• A Monte Carlo algorithm for spin foam intertwiners
• On the Hydrogen Atom in the Holographic Universe
• Quantum Groups and Polymer Quantum Mechanics