论文标题
多项式过滤的多体定位的精确对角线方法
Polynomially filtered exact diagonalization approach to many-body localization
论文作者
论文摘要
引入了用于大稀疏矩阵的多项式过滤的精确对角线化方法（polfed）。该算法找到了由特征值跨越特征值跨越特征值的最佳基础，该子空间通过使用矩阵的高阶多项式通过光谱转换接近指定的能量目标。与最先进的换挡方法相比，记忆需求比系统大小更好。证明了polfed的潜力，以检查一维相互作用的量子自旋1/2链中的多体定位跃迁。我们研究了您的无效时间的障碍强度和系统尺寸的缩放。两分纠缠熵和间隙比的系统大小依赖性突出了系统中有限尺寸效应的重要性。我们讨论了有关多体定位转变获得临界障碍强度的估计值的可能场景。
Polynomially filtered exact diagonalization method (POLFED) for large sparse matrices is introduced. The algorithm finds an optimal basis of a subspace spanned by eigenvectors with eigenvalues close to a specified energy target by a spectral transformation using a high order polynomial of the matrix. The memory requirements scale better with system size than in the state-of-the-art shift-invert approach. The potential of POLFED is demonstrated examining many-body localization transition in 1D interacting quantum spin-1/2 chains. We investigate the disorder strength and system size scaling of Thouless time. System size dependence of bipartite entanglement entropy and of the gap ratio highlights the importance of finite-size effects in the system. We discuss possible scenarios regarding the many-body localization transition obtaining estimates for the critical disorder strength.
