The density matrix renormalization group (DMRG) of White 1992 remains to this day an integral component of many state-of-the-art methods for efficiently simulating strongly correlated quantum systems. In quantum chemistry, QC-DMRG became a powerful tool for ab initio calculations with the non-relativistic Schrödinger equation. An important issue in QC-DMRG is the so-called ordering problem -- the optimal ordering of DMRG sites corresponding to electronic orbitals that produces the most accurate results. To this end, a commonly used heuristic is the grouping of strongly correlated orbitals as measured via quantum mutual information. In this work, we show how such heuristics can be directly related to minimizing the entanglement entropy of matrix product states and, consequently, to the truncation error of a fixed bond dimension approximation. Key to establishing this link is the strong subadditivity of entropy. This provides rigorous theoretical justification for the orbital ordering methods and suggests alternate ordering criteria.
Renormalization group and long-range conditional mutual information in hierarchical models
University of California at San Diego（圣地亚哥加利福尼亚大学）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣巴巴拉分校卡弗里理论物理研究所）
Essential difference between 2D and 3D from the perspective of real-space renormalization group
The University of Tokyo（东京大学）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Institut des Hautes Études Scientifiques (IHES)（高等科学研究所）；Trans-scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）
Renormalization group flows of Hamiltonians using tensor networks
利用张量网络构造了二维经典配分函数的哈密顿量的重整化群流。类似于张量网络重整化（[G. Evenbly和G. Vidal，Phys. Rev. Lett. 115，180405（2015）]，[S.杨志- C. Gu和X。- G Wen，Phys. Rev. Lett. 118，110504（2017）]），我们获得了临界状态下的近似不动点张量网络。然而，我们的形式主义保持积极的张量在每一步，因此产生的解释，在哈密尔顿流。我们强调，张量网络方法和Kadanoff的自旋阻塞方法之间的关键区别可以理解为在每一个抽取步骤中局部基的变化，这是克服互信息面积定律的关键属性。我们推导出代数关系的不动点张量，计算临界指数，并基准我们的方法上的伊辛模型和六顶点模型。
Site-Order Optimization in the Density Matrix Renormalization Group via Multi-Site Rearrangement
Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科）；Graduate School of Science and Technology, Gunma University（群马大学科学技术研究院）；Center for Quantum Information and Quantum Biology, The University of Osaka（大阪大学量子信息与量子生物学中心）；Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS)（RIKEN计算科学中心（R-CCS）计算材料科学研究组）
