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首页> 外文期刊>The Journal of Chemical Physics >Obtaining the two-body density matrix in the density matrix renormalization group method
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Obtaining the two-body density matrix in the density matrix renormalization group method

机译：在密度矩阵重归一化群方法中获得两体密度矩阵

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摘要

We present an approach that allows to produce the two-body density matrix during the density matrix renormalization group (DMRG) run without an additional increase in the current disk and memory requirements. The computational cost of producing the two-body density matrix is proportional to O(M(3)k(2)+M(2)k(4)). The method is based on the assumption that different elements of the two-body density matrix can be calculated during different steps of a sweep. Hence, it is desirable that the wave function at the convergence does not change during a sweep. We discuss the theoretical structure of the wave function ansatz used in DMRG, concluding that during the one-site DMRG procedure, the energy and the wave function are converging monotonically at every stEP 1of the sweep. Thus, the one-site algorithm provides an opportunity to obtain the two-body density matrix free from the N-representability problem. We explain the problem of local minima that may be encountered in the DMRG calculations. We discuss theoretically why and when the one- and two-site DMRG procedures may get stuck in a metastable solution, and we list practical solutions helping the minimization to avoid the local minima. (c) 2008 American Institute of Physics.
机译：我们提出了一种方法，该方法允许在密度矩阵重归一化组（DMRG）运行期间生成两体密度矩阵，而无需额外增加当前磁盘和内存的需求。产生两体密度矩阵的计算成本与O（M（3）k（2）+ M（2）k（4））成比例。该方法基于这样的假设：可以在扫描的不同步骤期间计算两体密度矩阵的不同元素。因此，期望在收敛期间波函数在扫描期间不改变。我们讨论了在DMRG中使用的波函数ansatz的理论结构，得出结论，在单站点DMRG过程中，能量和波函数在扫描的每个stEP 1处都单调收敛。因此，一站式算法提供了一个机会来获得没有N可表示性问题的两体密度矩阵。我们解释了DMRG计算中可能遇到的局部最小值问题。我们从理论上讨论了为什么一站式和两站式DMRG过程可能以及何时陷入亚稳态解决方案中，并且列出了有助于最小化以避免局部最小值的实用解决方案。 （c）2008年美国物理研究所。

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