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A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed.
Ising model in a transverse field. I. Basic theory
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Classical simulation of quantum many-body systems with a tree tensor network
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From quantum to classical molecular dynamics: reduced models and numerical analysis
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The geometry of algorithms using hierarchical tensors
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Alternating minimal energy methods for linear systems in higher dimensions
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Algorithm 941:
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Geometric structures in tensor representations (final release)
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Time integration in the multiconfiguration time-dependent Hartree method of molecular quantum dynamics
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Tensor spaces and numerical tensor calculus
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Time-evolution methods for matrix-product states
S. Paeckel, T. Köhler, A. Swoboda, S. R. Manmana, U. Schollwöck, and C. Hubig · 2019
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Time-dependent variational principle with ancillary Krylov subspace
M. Yang and S. R. White · 2020
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An unconventional robust integrator for dynamical low-rank approximation
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Time integration of tree tensor networks
G. Ceruti, C. Lubich, and H. Walach · 2021
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Matrix product states and projected entangled pair states: Concepts, symmetries, theorems
J. I. Cirac, D. Perez-Garcia, N. Schuch, and F. Verstraete · 2021
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Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations
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Unifying time evolution and optimization with matrix product states
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Discretized dynamical low-rank approximation in the presence of small singular values
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Tree-based tensor formats
A. Falcó, W. Hackbusch, and A. Nouy · 2018
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Time integration of rank-constrained Tucker tensors
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Rank-adaptive tensor methods for high-dimensional nonlinear PDEs
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Efficient bond-adaptive approach for finite-temperature open quantum dynamics using the one-site time-dependent variational principle for matrix product states
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Time evolution of ML–MCTDH wavefunctions. II. Application of the projector splitting integrator
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A rank-adaptive robust integrator for dynamical low-rank approximation
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