Time-dependent variational principle with ancillary Krylov subspace
Time-dependent variational principle with ancillary Krylov subspace
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DOI：
10.1103/physrevb.102.094315
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发表时间：
2020-05
影响因子：
3.7
通讯作者：
Ming-Jay Yang;S. White
中科院分区：
文献类型：
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作者：
Ming-Jay Yang;S. White
我们提出了一种改进方案，用于在二维系统或具有长程相互作用的一维系统的有限矩阵乘积状态（MPS）中执行时间相关变分原理（TDVP）。我们提出了一种在 MPS 中表示时间演化状态的方法，其基础通过全局 Krylov 向量的状态平均来丰富。我们表明，投影误差显着减小，因此即使使用更大的时间步长，仍然可以获得精确的时间演化。与单点 TDVP 相结合，我们的方法提供了一种动态增加键维数的方法，同时仍然保持实时演化的幺正性。我们的方法比传统的双位点 TDVP 更准确，并且键尺寸增长更慢。
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 both more accurate and has slower bond dimension growth than the conventional two-site TDVP.