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Non-invertible symmetry breaking in a frustration-free spin chain (2502.11997v1)
Published 17 Feb 2025 in hep-th, cond-mat.stat-mech, cond-mat.str-el, math-ph, and math.MP
Abstract: A nearest-neighbor, frustration-free spin $\frac{1}{2}$ chain can be constructed {\it 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.