Disorder-Free Localization from Gauss's Law in 2+1D Lattice Gauge Theories — E8 Intelligence Research

Abstract

FINDING: Disorder-free localization (DFL) in 2+1D lattice gauge theories arises from local gauge constraints (Gauss's law) and global symmetries, not random disorder, producing ergodicity breaking in translation-invariant systems. | MATH: Hamiltonian constraint: \( G_i |\psi\rangle = 0 \) for all sites \( i \), where \( G_i = \sum_{\text{links}} E_i^a - \rho_i \) (Gauss law). Symmetry sectors labeled by eigenvalues of \( G_i \). Localization length \( \xi \sim 1/\ln(\Delta E) \) from energy gaps between superselection sectors. No explicit disorder term \( \sum_i h_i \sigma_i^z \) needed. | CONNECTION: Gauge invariance imposes a local constraint algebra isomorphic to a root system of type \( A_{N-1} \) (SU(N) gauge group). The Hilbert space fragmentation mirrors the decomposition into weight spaces of the Lie algebra. The ratio of sector sizes follows combinatorial patterns (e.g., Catalan numbers for 1+1D U(1) gauge theory). No direct golden ratio or base-60 link. | DEPTH: 8 — DFL is a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com