Fusing binary interface defects in topological phases: The Z/pZ case

Abstract

A binary interface defect is any interface between two (not necessarily invertible) domain walls. We compute all possible binary interface defects in Kitaev's Z/pZ model and all possible fusions between them. Our methods can be applied to any Levin-Wen model. We also give physical interpretations for each of the defects in the Z/pZ model. These physical interpretations provide a new graphical calculus which can be used to compute defect fusion. *

Gauging defects in quantum spin systems: A case study

“…This is the essence of the 'inflation trick' developed in [BBJ18,BB19b,BB19a]. We refer the interested reader to these references for more details.…”

“…For fixed representation (fixed, x, y), we find a unique vector up to a multiplicative scalar for each α , so each morphism space is one dimensional. We define the basis to be The 'inflation trick' developed in [BBJ18,BB19b,BB19a] picks out the representation P 0,0 , and we work with that from here on. This means…”

Computing defects associated to bounded domain wall structures: the $\mathbb{Z}/p\mathbb{Z}$ case

“…In Ref. [36], we exclusively used the idempotent description. In this paper, we shall use both ways of presenting a representation of Ann.…”

“…Additionally, we gave an explicit physical interpretation of all bimodules for the case C = D = Vec(Z/pZ) for prime p. In Ref. [36], we extended this work to include binary interface defects. We showed how to compute the horizontal fusion (tensor product) and vertical fusion (composition) of these defects.…”

“…The authors have used the algorithm to check the horizontal and vertical fusion tables from Ref. [36] in the computer. In Section III, we discuss the domain wall associator.…”