Domain Walls in Topological Phases and the Brauer–Picard Ring for $${{\rm Vec} (\mathbb{Z}/p\mathbb{Z})}$$

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

“…We refer to Ref. [35] for the bimodule definitions for Vec(Z/pZ). Definitions of idempotents corresponding to all 2-string annular categories can be found in Ref.…”

“…We can also compute bimodule associators using the physical interpretations of the bimodules from Ref. [35] (Table II)…”

“…In Ref. [35], following Ref. [46], we gave a complete list of the simple Vec(Z/pZ)-bimodules (reproduced in Table I).…”

“…In Ref. [35], we showed how to compute the tensor product of C−D bimodules M ⊗ D N , corresponding to fusing the domain walls in the LW model. Additionally, we gave an explicit physical interpretation of all bimodules for the case C = D = Vec(Z/pZ) for prime p. In Ref.…”

Gauging defects in quantum spin systems: A case study

“…We now list all the Vec(Z/pZ)-Vec(Z/pZ) bimodules since we are going to need them in Subsection 2.3. This data is mostly taken from [BBJ19], and the names assigned to the bimodules are taken from there. Each bimodule M is labeled by a conjugacy class of subgroups H ⊆ Z/pZ × Z/pZ and a 2−cocycle ω ∈ H 2 (H, U (1)) (see [EGNO15]).…”