论文标题
多旋转系统中内部本本特征脑的Delta-Davidson方法
Delta-Davidson method for interior eigenproblem in many-spin systems
论文作者
论文摘要
已经开发了许多数值方法，例如张量化网络方法，包括密度矩阵重新归一化组计算，以计算量子多体系统的极端/接地状态。但是，很少有人关注中心国家，在系统规模方面，它们彼此之间彼此成倍接近。我们提出了一种Delta-Davidson（Deldav）方法，以在许多旋转系统中有效地找到此类内部（包括中央）状态。 Deldav方法在Chebyshev多项式扩展中利用了Delta滤波器，结合了子空间对角度化，以克服几乎退化的问题。在Ising自旋链和自旋玻璃碎片上进行的数值实验表明，在寻找内部状态和基态时，提出的方法的正确性，效率和鲁棒性。可以使用寻求的内部状态来识别多体定位阶段，量子混乱和极端的动力学结构。
Many numerical methods, such as tensor network approaches including density matrix renormalization group calculations, have been developed to calculate the extreme/ground states of quantum many-body systems. However, little attention has been paid to the central states, which are exponentially close to each other in terms of system size. We propose a Delta-Davidson (DELDAV) method to effciently find such interior (including the central) states in many-spin systems. The DELDAV method utilizes Delta filter in Chebyshev polynomial expansion combined with subspace diagonalization to overcome the nearly degenerate problem. Numerical experiments on Ising spin chain and spin glass shards show the correctness, effciency, and robustness of the proposed method in finding the interior states as well as the ground states. The sought interior states may be employed to identify many-body localization phase, quantum chaos, and extremely long-time dynamical structure.
