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Negative signs in many-body wavefunctions play an important role in quantummechanics. The ground-state wavefunction of double semion model on atwo-dimensional hexagonal lattice contains an intrinsic sign which cannot beremoved by any local transformation. Here we proposed a generic double semionwavefunction in tensor network representation, and the wavefunction norm ismapped to the partition function of a triangular lattice Ashkin-Teller modelwith imaginary magnetic fields and imaginary three-spin triangular faceinteractions. To solve this non-Hermitian model with parity-time (PT) symmetry,numerical tensor-network methods are employed, and a global phase diagram isdetermined. Adjacent to the double semion phase, we find a gapless dense loopphase described by non-unitary conformal field theory and a PT-symmetrybreaking phase with zeros of the partition function. So a connection hasestablished between the intrinsic signs in the topologically orderedwavefunction and the PT-symmetric non-Hermitian statistical model.

Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions