Emergent quantum electrodynamics from a three-dimensional bosonic lattice: Coulomb law, photons, and Fermi statistics without fundamental fermions

We study a three-dimensional periodic lattice model whose degrees of freedom are entirely bosonic — Gamma operators and compact U(1) rotors on each link — following the framework of Levin and Wen. Working on a cubic lattice with 64 vertices, 192 edges, and 960 rotor links, we demonstrate numerically that four hallmarks of quantum electrodynamics emerge simultaneously from a single set of local couplings: (i) a 1/r Coulomb interaction between static charges, derived analytically from the line-graph Green’s function and verified on lattices up to L=128; (ii) two transverse photon branches with linear dispersion; (iii) Fermi statistics of composite string-endpoint excitations, confirmed by 23,040 exact anticommutation checks and explicit seven-hop exchange paths; and (iv) a local conservation law that locks charge and flux degrees of freedom. We also identify an exact compensation symmetry of the full Hamiltonian that obstructs the readout of topological labels through native gauge-invariant observables.