Density matrix formulation for quantum renormalization groups.

By S. White. 1992

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “However, such a decomposition has been proposed earlier in the density-matrix renormalization group method (DMRG) for simulating quantum systems [235, 266].”
Exponential Decay of Correlations Implies Area Law (2012, methodology): “In fact, such a representation is more than of theoretical interest, as matrix product states are the variational ansatz for the most successful known method for simulating one-dimensional quantum systems, the Density Matrix Renormalization Group (DMRG) [39, 42].”
LOCAL CONVERGENCE OF ALTERNATING SCHEMES FOR OPTIMIZATION OF CONVEX PROBLEMS IN THE TT FORMAT (2011, methodology): “Also, it should be investigated, if on the basis of our present proof convergence of the promising DMRG algorithm [40, 38, 34], used for eigenvalue computations in quantum physics and investigated lately under the acronym MALS for more general optimization tasks in [20], also may be veri ed.”
Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory. (2016, methodology): “Recently, some of us performed DMRG-SCF calculations 48 on the model cluster with the cc-pVDZ basis set using an active space of (28e, 22o).”
Electronic structure calculations with dynamical mean-field theory (2005, unknown): “Phys., Vol. 78, No. 3, July–September 2006 Dagotto, 1994 , density-matrix renormalization-group methods White, 1992; Schollwöck, 2005 , and so on.”
Superfast Fourier Transform Using QTT Approximation (2012, methodology): “The orthogonality of interfaces is also used in DMRG algorithm [60].”
Low-rank tensor methods for linear systems and eigenvalue problems (2012, background): “Although these decompositions have predecessors in the computational chemistry and physics literature [74, 68], their use in numerical analysis has been explored only very recently.”
OpenMolcas: From source code to insight. (2019, methodology): “After White proposed the DMRG 101,102 in 1992, subsequent work 103 − 109 established that DMRG optimizes a matrix product state (MPS).”
Solving the quantum many-body problem with artificial neural networks (2016, background): “Compression approaches instead rely on ef-ﬁcient representations of the wave function, and most notably in terms of matrix product states (MPS) [4–6] or more general tensor networks [7, 8].”
Quantum Entanglement in Neural Network States (2017, background): “…of a number of eﬃcient classical algorithms for solving intricate many-body problems, e.g., DMRG (density-matrix renormalization group) [9, 17, 18], TEBD (time-evolving block decimation) [19], PEPS [10, 12] (projected entangled pair states), and MERA (multiscale entanglement…”
A Universal Operator Growth Hypothesis (2018, unknown): “As an example, the success of the density matrix renormalization group algorithm is a consequence of the area law of entanglement entropy [70, 71].”
Harnessing the Power of the Second Quantum Revolution (2020, methodology): “The power of the density-matrix renormalization group (DMRG) [146] derives from the eﬃcient representation of entanglement encoded in MPSs [147].”