Tensor networks and the numerical renormalization group
Tensor networks and the numerical renormalization group
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DOI：
10.1103/physrevb.86.245124
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发表时间：
2012-09
影响因子：
3.7
通讯作者：
A. Weichselbaum
中科院分区：
文献类型：
--
作者：
A. Weichselbaum
全密度矩阵数值重整化群（NRG）已经发展成为在NRG框架内计算任意温度下的热力学量的系统和透明的设置。它基于Anders和Schiller（2005）引入的完备基集直接评估了相关的莱曼表示。此外，通过明确和仔细地构建在能量壳分布上自然产生的全热密度矩阵，特别注意了从低能物理到高能的可能反馈。给出了谱函数（fdmNRG）、时变NRG （tdmNRG）、费米-黄金法则计算（fgrNRG）以及普通热力学期望值计算的具体例子。此外，基于这一事实，由于其迭代性质，NRG特征态自然地用矩阵积状态来描述，张量网络的语言在描述底层算法过程中被证明是非常方便的。因此，本文还从相应张量网络的角度对典型的NRG计算进行了详细的介绍和讨论。
The full-density-matrix numerical renormalization group (NRG) has evolved as a systematic and transparent setting for the cal- culation of thermodynamical quantities at arbitrary temperatures within the NRG framework. It directly evaluates the relevant Lehmann representations based on the complete basis sets intro- duced by Anders and Schiller (2005). In addition, specific attention is given to the possible feedback from low energy physics to high energies by the explicit and careful construction of the full thermal density matrix, naturally generated over a distribution of energy shells. Specific examples are given in terms of spectral functions (fdmNRG), time-dependent NRG (tdmNRG), Fermi-Golden rule calculations (fgrNRG), as well as the calculation of plain thermodynamic expectation values. Furthermore, based on the very fact that, by its iterative nature, the NRG eigenstates are naturally described in terms of matrix product states, the language of tensor networks has proven enormously convenient in the description of the underlying algorithmic procedures. This paper therefore also provides a detailed introduction and discussion of the prototypical NRG calculations in terms of their corresponding tensor networks.