论文标题
量子热化精确对角线化研究指南
Guide to Exact Diagonalization Study of Quantum Thermalization
论文作者
论文摘要
精确的对角线化是一种研究孤立量子多体系统的强大数值方法。本文提供了对数值算法的评论，以对角度化哈密顿矩阵。对称和保护法帮助我们有效地进行数值研究。我们解释了使用粒子数量保护，翻译对称性，粒子 - 孔对称性和空间反射对称性在Spin-1/2 XXZ模型或一维晶格中的硬核玻色子模型的背景下，使用粒子数量保守，翻译对称性，粒子 - 孔对称性和空间反射对称性来解释方法。我们还解释了研究由Schrödinger方程所控制的统一时间演化并计算热力学量（例如纠缠熵）的方法。作为一种应用，我们证明了支持XXZ模型中本征态热假设存在的数值结果。
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 holds in the XXZ model.
