Inversion Symmetry of Singular Values and a New Orbital Ordering Method in Tensor Train Approximations for Quantum Chemistry

DOI10.1137/20M1320122zbMath1462.81145arXiv2002.07459MaRDI QIDQ5147987

Mi-Song Dupuy, Gero Friesecke

Publication date: 29 January 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.07459

zbMATH Keywords

quantum chemistrydensity matrix renormalization grouptensor trainordering schemesdecay of singular values

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Eigenvalues, singular values, and eigenvectors (15A18) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) PDEs in connection with quantum mechanics (35Q40) Nonperturbative methods of renormalization applied to problems in quantum field theory (81T16) Perturbation theories for operators and differential equations in quantum theory (81Q15) Renormalization group methods applied to problems in quantum field theory (81T17) Many-body theory; quantum Hall effect (81V70) Molecular physics (81V55) Multilinear algebra, tensor calculus (15A69) Quantum coherence, entanglement, quantum correlations (81P40) Growth estimates (40E10) Special bases (entangled, mutual unbiased, etc.) (81P55)

Related Items (1)

Two-electron wavefunctions are matrix product states with bond dimension three

Uses Software

• CheMPS2
• Budapest QC-DMRG

Cites Work

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• CheMPS2: a free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry
• On the interconnection between the higher-order singular values of real tensors
• The density-matrix renormalization group in the age of matrix product states
• The multiconfiguration equations for atoms and molecules: charge quantization and existence of solutions
• On manifolds of tensors of fixed TT-rank
• MATRIX PRODUCT STATE REPRESENTATION FOR SLATER DETERMINANTS AND CONFIGURATION INTERACTION STATES
• The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
• Hierarchical Singular Value Decomposition of Tensors
• Tensor Spaces and Numerical Tensor Calculus
• Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
• Numerical tensor calculus
• Remainder terms for some quantum entropy inequalities

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