Exact solution of the three-dimensional (3D) Z2 lattice gauge theory

Abstract: In this work, the origin of nonlocal effects is inspected and the contributions of nontrivial topological structures to physical properties are investigated in details for both the 3D Ising model and the Z2 lattice gauge model. Then the exact solution for the 3D Z2 lattice gauge theory is derived by the duality between the two models. Several fundamental issues, such as dimensionality, duality, symmetry, manifold, degenerate states, are investigated for these many-body interacting spin systems. The connections with superfluid, superconductors, etc. are evaluated. Furthermore, physical significances and mathematical aspects of the 3D Z2 lattice gauge theory are discussed with respect to topology, geometry, and algebra.