Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry

Understand

We introduce the notion of combinatorial gauge symmetry -- a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states) -- that preserve the commutation and anti-commutation relations among the spins.

• We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated to the automorphism of these matrices with respect to monomial transformations.
• Armed with this symmetry, we address the physical problem of how to build quantum spin liquids with physically accessible interactions.
• In addition to its intrinsic physical significance, the problem is also tied to that of how to build topological qubits.