Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States

TL;DR

This paper introduces a novel method to construct non-Hermitian many-body Hamiltonians from matrix product states, enabling systematic exploration of non-Hermitian physics with preserved topological and chiral properties.

Contribution

It generalizes the parent Hamiltonian approach to non-Hermitian systems, allowing direct design of models with specific ground states and features.

Findings

Constructed a non-Hermitian spin-1 model from AKLT state

Preserves chiral order and symmetry-protected topological order

Provides a new framework for non-Hermitian many-body systems

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.