A new 'combinatorial gauge symmetry' lets two-body spin Hamiltonians with Hadamard coupling matrices realize exact local Z2 gauge symmetries and, in a limit, topological spin liquids and the X-cube fracton model.
Fracton topological order, generalized lattice gauge theory, and duality,
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Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry
A new 'combinatorial gauge symmetry' lets two-body spin Hamiltonians with Hadamard coupling matrices realize exact local Z2 gauge symmetries and, in a limit, topological spin liquids and the X-cube fracton model.