Key points are not available for this paper at this time.
In 1992, Kennedy and Tasaki constructed a nonlocal unitary transformation that maps between a Z₂Z₂ spontaneously symmetry breaking phase and the Haldane gap phase, which is a prototypical symmetry-protected topological (SPT) phase in modern framework, on an open spin chain. In this work, we propose a way to define it on a closed chain by sacrificing unitarity. The operator realizing such a nonunitary transformation satisfies noninvertible fusion rule and implements a generalized gauging of the Z₂Z₂ global symmetry. These findings connect the Kennedy-Tasaki transformation to numerous other concepts developed for SPT phases and opens a way to construct SPT phases systematically using the duality mapping.
Li et al. (Fri,) studied this question.