Low-rank Riemannian eigensolver for high-dimensional Hamiltonians
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2018-12
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Report
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Abstract
Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor methods have proven to be an efficient tool for the approximation of solutions of high-dimensional eigenvalue problems, however, their performance deteriorates quickly when the number of eigenstates to be computed increases. We address this issue by designing a new algorithm motivated by the ideas of Riemannian optimization (optimization on smooth manifolds) for the approximation of multiple eigenstates in the tensor-train format, which is also known as matrix product state representation. The proposed algorithm is implemented in TensorFlow, which allows for both CPU and GPU parallelization.
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2018-48
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Seminar for Applied Mathematics, ETH Zurich
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03435 - Schwab, Christoph / Schwab, Christoph
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