打破纠缠-结构权衡：多体局域化保护随机张量网络中的涌现引力几何
Breaking the Entanglement-Structure Trade-off: Many-Body Localization Protects Emergent Holographic Geometry in Random Tensor Networks
AI总结：
研究通过随机张量网络验证了引力几何与纠缠的关系，发现多体局域化保护了引力几何的涌现，突破了量子纠缠与结构之间的权衡。
摘要：
我们对随机张量网络（RTN）中的“纠缠几何引力”链进行了系统性数值研究，基于ER-EPR猜想和Jacobson的热力学推导。首先，验证了动量基础：纠缠第一定律δ⟨K⟩=δS（斜率=1.000），几何编码由互信息（相关性=0.92）以及引力扰动的局部性（3.3x）。我们还确认引力动力学（JT引力）并未出现，确定了动量-动力学的边界。第二，更重要的是，我们发现多体局域化（MBL）是保护涌现引力几何免于热化的机制。将Haar随机演化（几何寿命t≈6）替换为XXZ哈密顿量加局域扰动，我们观察到在扰动强度W_c≈10-12以上，互信息-晶格相关性持续无限（r>0.5对于t>50）。我们映射了整个参数空间：最佳区域是接近Ising各向异性Δ≈50，W=30，得到r=0.779±0.002（通过Δ∈[30,70]的精细扫描确认）；只有引力（RTN）初始状态维持几何，而产品、Neél和Bell对状态不维持。MBL保持纠缠的空间结构（相邻/非相邻MI比~2.6-4.2x vs. 热力学相中的1.0x），而不是其总量。与经典单元格自动机的比较揭示，MBL唯一打破了由量子多边形所施加的纠缠-结构权衡：经典系统只能在互信息微不足道的代价下获得空间结构，而MBL则维持两者。
英文摘要：
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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