Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States

Abstract

There are various research strategies used for non-Hermitian systems, which typically involve introducing non-Hermitian terms to pre-existing 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 to construct 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 (AKLT) 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 to explore new properties and phenomena in non-Hermitian physics.

arXiv comment14 pages, 10 figures, to appear in Physical Review Letters

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• Composite Quantum Phases in Non-Hermitian Systems
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix
• Determining non-Hermitian parent Hamiltonian from a single eigenstate
• Quantifying non-Hermiticity using single- and many-particle quantum properties