We develop a pre-geometric reconstruction framework in which quantum mechanics, entanglement structure, gauge symmetry, locality, Lorentzian spacetime geometry, gravitation, and physical constants emerge from recursively stabilized coherent Hilbert-relational organization. The framework begins from a primitive coherent substrate consisting of compositional accessibility relations and complex transport amplitudes. No background spacetime manifold, metric geometry, or particle ontology is assumed fundamentally. The central proposal is that coherent Hilbert structure is more fundamental than spacetime geometry. Observable spacetime emerges through projection stabilization: a physical stability-selection mechanism dynamically selecting recursively stable coherent sectors from deeper relational structure. Quantum mechanics emerges from norm-preserving coherent transport. Entanglement emerges from nonfactorizable relational closure. Gauge symmetry emerges as redundancy of coherent transport representation. Classicality emerges through decoherence and stability selection. Lorentzian geometry emerges statistically from projected accessibility organization. Gravitation emerges thermodynamically as equilibrium relaxation of projected geometry. The framework is presented not as a completed unified theory, but as a reconstruction program aimed at explaining why physical reality organizes itself through Hilbert structure, gauge redundancy, locality, spacetime geometry, and thermodynamic gravitational dynamics.
Abstract Intrinsically topologically ordered phases can host anyons. Here, we take the view that entanglement between anyons can give rise to an emergent geometry resembling Anti-de Sitter (AdS) space. We analyze the entanglement structure of fractionalized anyons using mutual information and interpret the results within this emergent geometric framework. As a concrete example, we consider pairs of e / 2 -charged semions that arise from instanton configurations in a disordered zigzag graphene nanoribbon. These fractional charges, located on opposite zigzag edges, show long-range quantum entanglement despite being spatially separated. We analyze the scale dependence of their entanglement and embed the ribbon into an AdS-like bulk geometry. In this setup, the entanglement structure defines minimal surfaces in the bulk, providing a geometric view of the edge correlations. This gives a holographic picture of fractionalized degrees of freedom in quasi-one-dimensional systems and shows how quantum entanglement can generate emergent geometry even without conformal symmetry.
Using measures of entanglement such as negativity and tangles we provide a detailed analysis of entanglement structures in pure states of non-interacting qubits. The motivation for this exercise primarily comes from holographic considerations, where entanglement is inextricably linked with the emergence of geometry. We use the qubit systems as toy models to probe the internal structure, and introduce some useful measures involving entanglement negativity to quantify general features of entanglement. In particular, our analysis focuses on various constraints on the pattern of entanglement which are known to be satisfied by holographic sates, such as the saturation of Araki–Lieb inequality (in certain circumstances), and the monogamy of mutual information. We argue that even systems as simple as few non-interacting qubits can be useful laboratories to explore how the emergence of the bulk geometry may be related to quantum information principles.
We present a systematic numerical investigation of the "entanglement geometry gravity" chain in random tensor networks (RTN) established by the ER EPR conjecture and Jacobson's thermodynamic derivation. First, we verify the kinematic foundation: the entanglement first law
δ⟨K⟩=δS (slope=1.000), the encoding of geometry by mutual information (correlation=0.92), and the locality of holographic perturbations (3.3x). We also confirm that gravitational dynamics (JT gravity) does not emerge, identifying a sharp kinematics-dynamics boundary. Second, and more importantly, we discover that many-body localization (MBL) is the mechanism that protects emergent holographic geometry from thermalization. Replacing Haar-random evolution (geometry lifetime
t∼6) with an XXZ Hamiltonian plus on-site disorder, we observe a finite-size crossover at disorder strength
Wc≈10−12 above which mutual-information-lattice correlations persist indefinitely (
r>0.5 for
t>50). We map the full parameter space: the optimal regime is a near-Ising anisotropy
Δ≈50 with
W=30 yielding
r=0.779±0.002 (confirmed by a fine scan over
Δ∈[30,70]); only holographic (RTN) initial states sustain geometry, while product, Néel, and Bell-pair states do not. MBL preserves the spatial structure of entanglement (adjacent/non-adjacent MI ratio ~2.6-4.2x vs. 1.0x in the thermal phase), rather than its total amount. A comparison with classical cellular automata reveals that MBL uniquely breaks the entanglement-structure trade-off imposed by quantum monogamy: classical systems achieve spatial structure only at the cost of negligible mutual information, while MBL sustains both.