论文标题
辅助Krylov子空间的时间依赖性变分原理
Time Dependent Variational Principle with Ancillary Krylov Subspace
论文作者
论文摘要
我们提出了一个改进的方案，以在有限矩阵乘积状态（MPS）的二维系统或具有远距离相互作用的一维系统中执行依赖时间的变分原理（TDVP）。我们提出了一种在国会议员中代表随时间不断发展的状态的方法，其基础通过与全球krylov载体的状态平均化丰富。我们表明，投影误差大大减少，因此即使使用了更大的时间步，仍然可以获得精确的时间演变。与一个站点的TDVP相结合，我们的方法提供了一种动态增加债券维度的方法，同时仍然保留实时演变的单位性。与常规的两个站点TDVP相比，我们的方法可以更准确，并且表现出较慢的键尺寸生长。
We propose an improved scheme to do the time dependent variational principle (TDVP) in finite matrix product states (MPS) for two-dimensional systems or one-dimensional systems with long range interactions. We present a method to represent the time-evolving state in a MPS with its basis enriched by state-averaging with global Krylov vectors. We show that the projection error is significantly reduced so that precise time evolution can still be obtained even if a larger time step is used. Combined with the one-site TDVP, our approach provides a way to dynamically increase the bond dimension while still preserving unitarity for real time evolution. Our method can be more accurate and exhibit slower bond dimension growth than the conventional two-site TDVP.
