Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Effective Geometry of Bell-Network States on a Dipole Graph(Institute of Physics, 2025) Baytaş, Bekir; Yokomizo, N.; 01. Izmir Institute of TechnologyBell-network states are a class of entangled states of the geometry that satisfy an area-law for the entanglement entropy in a limit of large spins and are automorphism-invariant, for arbitrary graphs. We present a comprehensive analysis of the effective geometry of Bell-network states on a dipole graph. Our main goal is to provide a detailed characterization of the quantum geometry of a class of diffeomorphism-invariant, area-law states representing homogeneous and isotropic configurations in loop quantum gravity, which may be explored as boundary states for the dynamics of the theory. We found that the average geometry at each node in the dipole graph does not match that of a flat tetrahedron. Instead, the expected values of the geometric observables satisfy relations that are characteristic of spherical tetrahedra. The mean geometry is accompanied by fluctuations with considerable relative dispersion for the dihedral angle, and perfectly correlated for the two nodes. © 2024 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.Article Citation - WoS: 2Citation - Scopus: 2Cosmological States in Loop Quantum Gravity on Homogeneous Graphs(American Physical Society, 2023) Baytaş, Bekir; Yokomizo, N.; 01. Izmir Institute of TechnologyWe introduce a class of states characterized by proposed conditions of homogeneity and isotropy in loop quantum gravity and construct concrete examples given by Bell-network states on a special class of homogeneous graphs. Such states provide new representations of cosmological spaces that can be explored for the formulation of cosmological models in the context of loop quantum gravity. We show that their local geometry is described in an automorphism-invariant manner by one-node observables analogous to the one-body observables used in many-body quantum mechanics, and compute the density matrix representing the restriction of global states to the algebra of one-node observables. The von Neumann entropy of this density matrix provides a notion of entanglement entropy of a local region that is invariant under automorphisms and can be applied to states involving superpositions of distinct graphs. © 2023 American Physical Society.