Unifying time evolution and optimization with matrix product states
Unifying time evolution and optimization with matrix product states
复制标题
DOI：
10.1103/physrevb.94.165116
复制
发表时间：
2016-10-10
影响因子：
3.7
通讯作者：
Verstraete, Frank
中科院分区：
文献类型：
--
作者：
Haegeman, Jutho;Lubich, Christian;Verstraete, Frank
我们表明，时间相关的变分原理提供了一个统一的框架，时间演化方法和优化方法的背景下，矩阵产品状态。特别是，我们引入了一个新的集成方案，用于研究时间演化，它可以科普任意的哈密顿量，包括那些与长程相互作用。而不是一个Suzuki-Trotter分裂的哈密顿量，这是背后的想法自适应时间相关的密度矩阵重整化群方法或时间演化块抽取，我们的方法是基于分裂的投影到矩阵产品状态切空间，因为它出现在Dirac-Frenkel时间相关的变分原理。我们讨论了所得到的算法类似于密度矩阵重整化群（DMRG）算法寻找基态如此紧密，它可以通过改变几行代码来实现，它继承了相同的稳定性和效率。特别是，我们的方法是兼容的任何哈密顿基态DMRG可以有效地实现。实际上，DMRG是我们的无限时间步长虚时间演化方案的一个特例。
We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimization methods in the context of matrix product states. In particular, we introduce a new integration scheme for studying time evolution, which can cope with arbitrary Hamiltonians, including those with long-range interactions. Rather than a Suzuki-Trotter splitting of the Hamiltonian, which is the idea behind the adaptive time-dependent density matrix renormalization group method or time-evolving block decimation, our method is based on splitting the projector onto the matrix product state tangent space as it appears in the Dirac-Frenkel time-dependent variational principle. We discuss how the resulting algorithm resembles the density matrix renormalization group (DMRG) algorithm for finding ground states so closely that it can be implemented by changing just a few lines of code and it inherits the same stability and efficiency. In particular, our method is compatible with any Hamiltonian for which ground-state DMRG can be implemented efficiently. In fact, DMRG is obtained as a special case of our scheme for imaginary time evolution with infinite time step.