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

Negative signs in many-body wavefunctions play an important role in quantum mechanics because interference relies on cancellation between amplitudes of opposite signs. The ground-state wavefunction of double semion model contains negative signs that cannot be removed by any local transformation. Here we study the quantum effects of these intrinsic negative signs. By proposing a generic double semion wavefunction in tensor network representation, we show that its norm can be mapped to the partition function of a triangular lattice Ashkin-Teller model with imaginary interactions. We use numerical tensor-network methods to solve this non-Hermitian model with parity-time symmetry and determine a global phase diagram. In particular, we find a dense loop phase described by non-unitary conformal field theory and a parity-time-symmetry breaking phase characterized by the zeros of the partition function. Therefore, our work establishes a connection between the intrinsic signs in the topological wavefunction and non-unitary phases in the parity-time-symmetric non-Hermitian statistical model. While negative signs in wave functions are known to play a relevant role in many-body quantum mechanics, their physical consequences on the nature of topologically ordered phases of matter is still unclear. Here, the authors use tensor network methods to show that the intrinsic negative signs of the double semion model are responsible for the non-unitary phases and non-unitary phase transitions found in the phase diagram. [ABSTRACT FROM AUTHOR]