Typicality in spin network states of quantum geometry

Abstract

In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network; however, they are mainly motivated by the fact that spin-network states can describe states of quantum geometry, providing a gauge-invariant basis for the kinematical Hilbert space of several background-independent approaches to quantum gravity. The first result is, by itself, the existence of a regime in which we show the emergence of a typical state. We interpret this as the proof that in that regime there are certain (local) properties of quantum geometry which are "universal". Such a set of properties is heralded by the typical state, of which we give the explicit form. This is our second result. In the end, we study some interesting properties of the typical state, proving that the area law for the entropy of a surface must be satisfied at the local level, up to logarithmic corrections which we are able to bound.

Typos and mistakes fixed

References in corpus (6)

• Typicality for Generalized Microcanonical Ensembles
• Polyhedra in loop quantum gravity
• Entanglement Entropy in Loop Quantum Gravity
• Horizon entropy from quantum gravity condensates
• A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
• Squeezed vacua in loop quantum gravity

Cited by in corpus (15)

• Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
• Entanglement entropy of Bell-network states in LQG: Analytical and numerical results
• Thermal quantum gravity condensates in group field theory cosmology
• Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
• On the fate of the Hoop Conjecture in quantum gravity
• Holographic maps from quantum gravity states as tensor networks
• Emergent Space-Time via a Geometric Renormalization Method
• Hidden Messenger from Quantum Geometry: Towards Information Conservation in Quantum Gravity
• From Coarse-Graining to Holography in Loop Quantum Gravity
• Loop Quantum Gravity's Boundary Maps
• Bulk area law for boundary entanglement in spin network states: entropy corrections and horizon-like regions from volume correlations
• Intertwiner Entanglement Excitation and Holonomy Operator
• Curvature from multipartite entanglement in quantum gravity states
• Deformations of Lorentzian Polyhedra: Kapovich-Millson phase space and SU(1,1) Intertwiners
• Thermofield Double States in Group Field Theory