Speaker
Han Yan
Description
Extended operators provide a useful probe of nonperturbative phases in lattice systems. I will introduce a family of (3+1)-dimensional qutrit models obtained by adding constrained spatial randomness to Haah’s cubic code. I prove that these models retain the absence of string logical operators, while numerical evidence shows that the self-similar fractal structure of the translation-invariant model is also lost. Instead, the logical sectors are generated by membrane-like operators. These results demonstrate that translation symmetry plays an essential role in organizing fractal operator structure and suggest a class of spatially nonuniform phases beyond conventional topological and fracton order.