2025/01/24 by Eck, Luisa
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2501.14722
Fusion surface models generalize the concept of anyon chains to 2+1 dimensions, utilizing fusion 2-categories as their input. We investigate bond-algebraic dualities in these systems and show that distinct module tensor categories M over the same braided fusion category B give rise to dual lattice models. This extends the 1+1d result that dualities in anyon chains are classified by module categories over fusion categories. We analyze two concrete examples: (i) a Rep(S3) model with a constrained Hilbert space, dual to the spin-\tfrac12 XXZ model on the honeycomb lattice, and (ii) a bilayer Kitaev honeycomb model, dual to a spin-\tfrac12 model with XXZ and Ising interactions. Unlike regular M=B fusion surface models, which conserve only 1-form symmetries, models constructed from M ≠ B can exhibit both 1-form and 0-form symmetries, including non-invertible ones.