Exploiting matrix symmetries and physical symmetries in matrix product states and tensor trains

DOI10.1080/03081087.2012.663371zbMath1270.15026arXiv1301.0746OpenAlexW1990448878MaRDI QIDQ4908163

K. Waldherr, Th. Schulte-Herbrüggen, Thomas Kilian Huckle

Publication date: 4 March 2013

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.0746

zbMATH Keywords

symmetric matricesspin Hamiltonianquantum many-body systemsmatrix product statespersymmetric matricestensor trainstensor chains

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Many-body theory; quantum Hall effect (81V70) Multilinear algebra, tensor calculus (15A69)

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Cites Work

• Tensor-Train Decomposition
• The density-matrix renormalization group in the age of matrix product states
• \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
• Matrix exponentials and parallel prefix computation in a quantum control problem
• Two soluble models of an antiferromagnetic chain
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
• Properties of the Eigenvectors of Persymmetric Matrices with Applications to Communication Theory
• Any Circulant-Like Preconditioner for Multilevel Matrices Is Not Superlinear