Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States

• URL: http://arxiv.org/abs/2301.12448v2
• Date: Wed, 10 May 2023 06:38:05 GMT
• Title: Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States
• Authors: Ruohan Shen, Yuchen Guo, Shuo Yang
• Abstract summary: We propose a new method to construct non-Hermitian many-body systems by generalizing the parent Hamiltonian method into non-Hermitian regimes. We demonstrate this method by constructing a non-Hermitian spin-$1$ model from the asymmetric Affleck-Kennedy-Lieb-Tasaki state.
• Score: 23.215516392012184
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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