Anyon condensation web and multipartite entanglement in two-dimensional modulated gauge theories
Guilherme Delfino, Yizhi You
Abstract
In this work we introduce an anyon condensation web that interconnects a broad class of two-dimensional (2D) finite gauge theories with multipolar conservation laws at a microscopic level. We refer to such theories as spatially modulated since their generators act nonuniformly across the system and have a strong position dependence. We find that condensation of appropriate set of anyons triggers the emergence of additional spatially modulated symmetries, which has the general effect of increasing the number of super-selection anyon sectors. As explicit examples, we start with the rank-2 toric code model and implement various anyon condensation protocols, resulting in a range of 2D higher-rank theories, each with a distinct gauge structure. We also expand the scope of anyon condensation by introducing lattice defects into spatially modulated theories and demonstrate that these geometric defects can be viewed as effective anyon condensations along the branch cut. Furthermore, we introduce the Multipartite Entanglement Mutual Information measure as a diagnostic tool to differentiate among various distinct multipole conserving phases. A captivating observation is the ultraviolet sensitivity of the mutual information sourced from multipartite entanglement in such modulated gauge theories, which depends on the geometric cut and the system size, and exhibits periodic oscillations at large distances.