Matrix-product-state comparison of the numerical renormalization group and the variational formulation of the density-matrix renormalization group
Matrix-product-state comparison of the numerical renormalization group and the variational formulation of the density-matrix renormalization group
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DOI：
10.1103/physrevb.78.035124
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发表时间：
2008-04
影响因子：
3.7
通讯作者：
H. Saberi;A. Weichselbaum;J. Delft
中科院分区：
文献类型：
--
作者：
H. Saberi;A. Weichselbaum;J. Delft
威尔逊数值重整化群！用NRG方法求解量子杂质模型，得到了一组具有矩阵乘积态形式的能量本征态。MPS”。白色的密度矩阵重整化群！用于处理量子晶格问题的“DMRG”同样可以根据MPS重新表述。因此，后者构成了两种方法的共同代数结构。我们利用这一事实比较单杂质安德森模型的NRG方法与变分矩阵乘积态方法！VMPS”，相当于单站点DMRG。对于后者，我们使用一个“展开”威尔逊链，这带来了显着减少数值成本相比，NRG。我们表明，所有的NRG本征态！“保留和丢弃”可以使用VMPS再现，并且比较两种方法的截断标准的差异，即能量空间中的尖锐与平滑。最后，我们证明，NRG的结果可以系统地进行变分优化的变分矩阵产品状态的空间，使用NRG作为输入产生的状态。
Wilson’s numerical renormalization group ! NRG" method for solving quantum impurity models yields a set of energy eigenstates that have the form of matrix product states ! MPS" . White’s density-matrix renormalization group ! DMRG" for treating quantum lattice problems can likewise be reformulated in terms of MPS. Thus, the latter constitute a common algebraic structure for both approaches. We exploit this fact to compare the NRG approach for the single-impurity Anderson model with a variational matrix product state approach ! VMPS" , equivalent to single-site DMRG. For the latter, we use an “unfolded” Wilson chain, which brings about a significant reduction in numerical costs compared to those of NRG. We show that all NRG eigenstates ! kept and discarded" can be reproduced using VMPS, and compare the difference in truncation criteria, sharp vs smooth in energy space, of the two approaches. Finally, we demonstrate that NRG results can be improved upon systematically by performing a variational optimization in the space of variational matrix product states, using the states produced by NRG as input.