Galois conjugates of String-net Model

Understand

We revisit a class of non-Hermitian topological models that are Galois conjugates of their Hermitian counter parts.

• Particularly, these are Galois conjugates of unitary string-net models.
• We demonstrate these models necessarily have real spectra, and that topological numbers are recovered as matrix elements of operators evaluated in appropriate bi-orthogonal basis, that we conveniently reformulate as a concomitant Hilbert space here.
• We also compute in the bi-orthogonal basis thetopological entanglement entropy, demonstrating that its real part is related to the quantum dimension of the topological order.