Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States

Ruohan Shen, Yuchen Guo, and Shuo Yang
Phys. Rev. Lett. 130, 220401 – Published 30 May 2023
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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.

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  • Received 1 February 2023
  • Revised 28 March 2023
  • Accepted 9 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.220401

© 2023 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Ruohan Shen1, Yuchen Guo1, and Shuo Yang1,2,3,*

  • 1State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
  • 2Frontier Science Center for Quantum Information, Beijing 100084, China
  • 3Hefei National Laboratory, Hefei 230088, China

  • *shuoyang@tsinghua.edu.cn

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Issue

Vol. 130, Iss. 22 — 2 June 2023

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