Kavli Affiliate: Masahito Yamazaki
| First 5 Authors: Weiguang Cao, Yuan Miao, Masahito Yamazaki, ,
| Summary:
Non-invertible dualities/symmetries have become an important tool in the
study of quantum field theories and quantum lattice models in recent years. One
of the most studied examples is non-invertible dualities obtained by gauging a
discrete group. When the physical system has more global symmetries than the
gauged symmetry, it has not been thoroughly investigated how those global
symmetries transform under non-invertible duality. In this paper, we study the
change of global symmetries under non-invertible duality of gauging a discrete
group $G$ in the context of (1+1)-dimensional quantum lattice models. We obtain
the global symmetries of the dual model by focusing on different Hilbert space
sectors determined by the $mathrm{Rep}(G)$ symmetry. We provide general
conjectures of global symmetries of the dual model forming an algebraic ring of
the double cosets. We present concrete examples of the XXZ models and the
duals, providing strong evidence for the conjectures.
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