Variational Matrix Product State Approach for Non-Hermitian System Based on a Companion Hermitian Hamiltonian

• URL: http://arxiv.org/abs/2210.14858v1
• Date: Wed, 26 Oct 2022 17:00:28 GMT
• Title: Variational Matrix Product State Approach for Non-Hermitian System Based on a Companion Hermitian Hamiltonian
• Authors: Zhen Guo, Zheng-Tao Xu, Meng Li, Li You, Shuo Yang
• Abstract summary: We propose an algorithm for solving the ground state of a non-Hermitian system in the matrix product state (MPS) formalism. If the eigenvalues of the non-Hermitian system are known, the companion Hermitian Hamiltonian can be directly constructed and solved.
• Score: 15.165363050850857
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Non-Hermitian systems exhibiting topological properties are attracting growing interest. In this work, we propose an algorithm for solving the ground state of a non-Hermitian system in the matrix product state (MPS) formalism based on a companion Hermitian Hamiltonian. If the eigenvalues of the non-Hermitian system are known, the companion Hermitian Hamiltonian can be directly constructed and solved using Hermitian variational methods. When the eigenvalues are unknown, a gradient descent along with the companion Hermitian Hamiltonian yields both the ground state eigenenergy and the eigenstate. With the variational principle as a solid foundation, our algorithm ensures convergence and provides results in excellent agreement with the exact solutions of the non-Hermitian Su-Schrieffer-Heeger (nH-SSH) model as well as its interacting extension. The approach we present avoids solving any non-Hermitian matrix and overcomes numerical instabilities commonly encountered in large non-Hermitian systems.

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