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arXiv · 2210.14858

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

Zhen Guo·Zheng-Tao Xu·Meng Li·Li You·Shuo Yang
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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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Zhen Guo, Zheng-Tao Xu, Meng Li, Li You, Shuo Yang. 2022-10-26. Variational Matrix Product State Approach for Non-Hermitian System Based on a Companion Hermitian Hamiltonian. https://arxiv.org/abs/2210.14858

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