论文标题
基于同伴Hermitian Hamiltonian的非热系统的变异矩阵产品状态方法
Variational Matrix Product State Approach for Non-Hermitian System Based on a Companion Hermitian Hamiltonian
论文作者
论文摘要
表现出拓扑特性的非热门系统正在吸引日益增长的兴趣。在这项工作中，我们提出了一种算法，用于解决基于同伴Hermitian Hamiltonian的基质产品状态（MPS）形式主义中的非甲米系统的基态。如果已知非热系统的特征值，则可以使用Hermitian变异方法直接构建和解决伴随的Hermitian Hamiltonian。当特征值尚不清楚时，梯度下降与同伴Hermitian Hamiltonian同时产生基态特征烯类和特征态。我们的算法以差异原理为坚实的基础，可确保收敛，并与非硫磺su-schrieffer-heeger（NH-SSH）模型的精确解决方案以及其相互作用的扩展非常吻合。我们提出的方法避免了解决任何非热矩阵，并克服了在大型非热系统中通常遇到的数值不稳定性。
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.
