Guide to Exact Diagonalization Study of Quantum Thermalization
Guide to Exact Diagonalization Study of Quantum Thermalization
复制标题
量子热化精确对角化研究指南
DOI：
--
复制
发表时间：
2020
影响因子：
0.6
通讯作者：
J. Noh
中科院分区：
文献类型：
--
作者：
Jung;J. Noh
精确对角化是研究孤立量子多体系统的一种强有力的数值方法。本文综述了哈密顿矩阵对角化的数值算法。对称性和守恒定律帮助我们有效地进行数值研究。我们解释的方法块对角化的哈密顿矩阵，通过使用粒子数守恒，平移对称性，粒子-空穴对称性，和空间反射对称性的背景下，自旋1/2 XXZ模型或硬核玻色子模型在一维晶格。我们还解释了研究薛定谔方程支配的幺正时间演化和计算纠缠熵等热力学量的方法。作为一个应用，我们证明了数值结果，支持本征态热化假设（ETH）在XXZ模型。
Exact diagonalization is a powerful numerical method to study isolated quantum many-body systems. This paper provides a review of numerical algorithms to diagonalize the Hamiltonian matrix. Symmetry and the conservation law help us perform the numerical study efficiently. We explain the method to block-diagonalize the Hamiltonian matrix by using particle number conservation, translational symmetry, particle-hole symmetry, and spatial reflection symmetry in the context of the spin-1/2 XXZ model or the hard-core boson model in a one-dimensional lattice. We also explain the method to study the unitary time evolution governed by the Schrödinger equation and to calculate thermodynamic quantities such as the entanglement entropy. As an application, we demonstrate numerical results that support that the eigenstate thermalization hypothesis (ETH) holds in the XXZ model.