Breaking the Entanglement-Structure Trade-off: Many-Body Localization Protects Emergent Holographic Geometry in Random Tensor Networks

• URL: http://arxiv.org/abs/2604.04596v1
• Date: Mon, 06 Apr 2026 11:20:08 GMT
• Title: Breaking the Entanglement-Structure Trade-off: Many-Body Localization Protects Emergent Holographic Geometry in Random Tensor Networks
• Abstract summary: We investigate the "entanglement geometry gravity" chain in random tensor networks (RTN)<n>Many-body localization is the mechanism that protects emergent holographic geometry from thermalization.<n>A comparison with classical cellular automata reveals that MBL uniquely breaks the entanglement-structure trade-off imposed by quantum monogamy.
• Score: 0.7310043452300737
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $δ\langle K\rangle=δS$ (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 $t\sim6$) with an XXZ Hamiltonian plus on-site disorder, we observe a finite-size crossover at disorder strength $W_c\approx10-12$ 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 $Δ\approx50$ with $W=30$ yielding $r=0.779\pm0.002$ (confirmed by a fine scan over $Δ\in[30,70]$); 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.

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