  Negative signs in many-body wavefunctions play an important role in quantum
mechanics. The ground-state wavefunction of double semion model on a
two-dimensional hexagonal lattice contains an intrinsic sign which cannot be
removed by any local transformation. Here we proposed a generic double semion
wavefunction in tensor network representation, and the wavefunction norm is
mapped to the partition function of a triangular lattice Ashkin-Teller model
with imaginary magnetic fields and imaginary three-spin triangular face
interactions. To solve this non-Hermitian model with parity-time (PT) symmetry,
numerical tensor-network methods are employed, and a global phase diagram is
determined. Adjacent to the double semion phase, we find a gapless dense loop
phase described by non-unitary conformal field theory and a PT-symmetry
breaking phase with zeros of the partition function. So a connection has
established between the intrinsic signs in the topologically ordered
wavefunction and the PT-symmetric non-Hermitian statistical model.
