Question

Is the string-net model Hermitian?

Answer 1

In Kitaev and Kong's paper, they define the Hermitian inner product on morphism spaces in Eq. (11). My question is that: Given that F symbols satisfy the pentagon identity, does that the string-net Hamiltonian (13) is Hermitian follow from the Hermitian inner product on morphism spaces? Is any related math theorem about the Hermiticity of Hamiltonian and the Hermitian inner product on morphism spaces

Answer 2

$<b><i>The bulk part is constructed using a unitary tensor category  as in the Levin-Wen model, whereas the boundary is associated with a module category over . We also consider domain walls (or defect lines) between different bulk phases. A domain wall is transparent to bulk excitations if the corresponding unitary tensor categories are Morita equivalent. Defects of higher codimension will also be studied. In summary, we give a dictionary between physical ingredients of lattice models and tensor-categorical notions.$