Dynamical Neighborhood Topology Effective Field Theory: Emergent Spacetime and Lorentz Invariance from a Discrete Quantum Lattice 动力学邻域拓扑有效场论:从离散量子晶格涌现的时空与洛伦兹不变性

The unification of general relativity (GR) and quantum mechanics (QM) remains the central open problem in theoretical physics. This work proposes the Dynamical Neighborhood Topology Effective Field Theory (DNTES), a framework that derives 3+1-dimensional continuous spacetime, Lorentz invariance, and the weak equivalence principle from a discrete O(2) quantum rotor lattice, with no prior assumptions of spacetime structure or relativistic symmetry. Based on the exact functional renormalization group (FRG) via the Wetterich equation, we prove to all orders that the dynamical critical index z ≡ 1 holds independently of the infrared cutoff scheme, enforcing emergent Lorentz invariance in the infrared limit. The analytical prediction is validated via unbiased SSE-QMC simulations, with the measured z = 1.002 ± 0.026 in full agreement with the theoretical result. We further give a falsifiable prediction for Lorentz invariance violation (LIV) at ultra-high energies, directly testable by the LHAASO observatory. Keywords: Emergent spacetime, quantum gravity, functional renormalization group, quantum phase transitions, Lorentz invariance, analogue gravity This is a first communication of a developing research program. The author is an independent researcher. Feedback and discussion are welcome.