Abstract: If a uniform 2D tensor network has C4v symmetry, should its contraction be trivial? In this talk, I will argue that the answer is no. Even in this highly constrained setting, the corner can carry hidden structure that is invisible from the usual edge viewpoint and can reorganize the boundary fixed point in qualitatively different ways. I will use the \pi-flux toric code and the eight-vertex model to illustrate how this happens, and then explain why it matters in practice: hidden algebraic sectors can affect CTMRG convergence and mislead iPEPS optimization. 

Contact: Lei Wang 9853