Abstract
There are various research strategies used for non-Hermitian systems, which typically involve introducing non-Hermitian terms to preexisting Hermitian Hamiltonians. It can be challenging to directly design non-Hermitian many-body models that exhibit unique features not found in Hermitian systems. In this Letter, we propose a new method for constructing non-Hermitian many-body systems by generalizing the parent Hamiltonian method into non-Hermitian regimes. This allows us to build a local Hamiltonian using given matrix product states as its left and right ground states. We demonstrate this method by constructing a non-Hermitian spin-1 model from the asymmetric Affleck-Kennedy-Lieb-Tasaki state, which preserves both chiral order and symmetry-protected topological order. Our approach opens up a new paradigm for systematically constructing and studying non-Hermitian many-body systems, providing guiding principles for exploring new properties and phenomena in non-Hermitian physics.
- Received 1 February 2023
- Revised 28 March 2023
- Accepted 9 May 2023
DOI:https://doi.org/10.1103/PhysRevLett.130.220401
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