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

• URL: http://arxiv.org/abs/2005.03841v2
• Date: Tue, 7 Jul 2020 02:12:14 GMT
• Title: Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
• Authors: Qi Zhang, Wen-Tao Xu, Zi-Qi Wang, and Guang-Ming Zhang
• Abstract summary: Ground-state wavefunction of double semion model on a two-dimensional hexagonal lattice contains an intrinsic sign. A connection has established between the intrinsic signs in the topologically ordered wavefunction and the PT-symmetric non-Hermitian statistical model.
• Score: 12.453831188907797
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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