Elliot Hu: Combinatorial Gauge Symmetry

Combinatorial gauge symmetry is a principle that allows us to construct lattice gauge theories with two key and distinguishing properties: a) only one- and two-body interactions are needed; and b) the symmetry is exact rather than emergent in an effective or perturbative limit. The ground state exhibits topological order for a range of parameters. This work generalizes this construction into a framework that encompasses any finite gauge group, Abelian or non-Abelian. The case of Abelian gauge groups is presented first, revealing in the process the fundamental mathematical structure of combinatorial gauge symmetry. The framework is then extended to encompass generic non-Abelian groups, which require additional mathematical tools. In addition to the general mathematical construction, a physical implementation in superconducting wire arrays, which offers a route to the experimental realization of lattice gauge theories with static Hamiltonians.