Author(s): Wenjie Ji (纪文杰), Ryan A. Lanzetta, Zheng Zhou (周正), and Chong Wang (王翀) The toric code, when deformed in a way that preserves the self-duality ${\mathbb{Z}}_{2}$ symmetry exchanging the electric and magnetic excitations, admits a transition to a topologically trivial state that spontaneously breaks the ${\mathbb{Z}}_{2}$ symmetry. Numerically, this transition was found … [Phys. Rev. Lett. 137, 086505] Published Thu Aug 20, 2026