We apply the tensor cross interpolation (TCI) algorithm to solve equilibrium quantum impurity problems with high precision based on the weak-coupling expansion. The TCI algorithm, a kind of active learning method, factorizes high-dimensional integrals that appear in the perturbative expansion into a product of low-dimensional ones, enabling us to evaluate higher-order terms efficiently. This method is free from the sign problem which quantum Monte Carlo methods sometimes suffer from, and allows one to directly calculate the free energy. We benchmark the TCI impurity solver on an exactly solvable impurity model, and find good agreement with the exact solutions. We also incorporate the TCI impurity solver into the dynamical mean-field theory to solve the Hubbard model, and show that the metal-to-Mott insulator transition is correctly described with comparable accuracy to the Monte Carlo methods. Behind the effectiveness of the TCI approach for quantum impurity problems lies the fact that the integrands in the weak-coupling expansion naturally have a low-rank structure in the tensor-train representation.
Tree tensor network impurity solver based on Cayley-tree mapping
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Probing quantum critical crossover via impurity renormalization group
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室和物理系）；School of Physics, Renmin University of China（中国人民大学物理学院）；Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（教育部量子态构建与操控重点实验室（中国人民大学））；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Jiangsu Physical Science Research Center（江苏物理科学研究中心）；Hefei National Laboratory（合肥国家实验室）
Improved time-translationally invariant tensor network influence functional method for Anderson impurity problems
State Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China（中国科学技术大学精密与智能化学国家重点实验室）；College of Science, National University of Defense Technology（国防科技大学理学院）
Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
