Non-invertible symmetry breaking in a frustration-free spin chain
Abstract
A nearest-neighbor, frustration-free spin 12 chain can be constructed via projectors of various ranks \'a la Bravyi-Gosset. We show that in the rank 1 case this system is gapped and has two ground states resembling ferromagnetic states. These states spontaneously break the non-invertible symmetry connecting them. The latter is proved using the machinery of algebraic quantum theory. The non-invertible symmetries of this system do not come from a duality.
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