Controlling the accuracy of the density-matrix renormalization-group method: The dynamical block state selection approach

By Ors Legeza, J. Roder, B. A. Hess. 2002

206 citations recorded by the source corpus.

We have applied the momentum space version of the density-matrix renormalization-group method (k-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in this new context. We have shown numerically that it is possible to determine the desired accuracy of the method in advance of the calculations by dynamically controlling the truncation error and the number of block states using a novel protocol that we dubbed dynamical block state selection protocol. The relationship between the real error and truncation error has been studied as a function of the number of orbitals and the fraction of filled orbitals. We have calculated the ground state of the molecules CH 2 , H 2 O, and F 2 as well as the first excited state of CH 2 . Our largest calculations were carried out with 57 orbitals, the largest number of block states was 1500-2000, and the largest dimensions of the Hilbert space of the superblock configuration was 800 0000-1 200 000.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/ec419d846edb465bf509e45e3122b708088f92da

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

The density matrix renormalization group in quantum chemistry. (2011, methodology): “With the development of an efficient parallel implementation of the DMRG, the possibility of using the DMRG for a brute-force near-exact solution of the Schrödinger equation (beyond the capabilities of standard FCI) began to be explored (21, 28, 33, 35, 36).”
The density-matrix renormalization group (2004, methodology): “…accuracy of 1 mH with errors between 4.1 and 0.2 mH, DMRG results of various groups sWhite and Martin, 1999; Daul, Ciofini, et al., 2000; Chan and Head-Gordon, 2002d are better than 0.2 mH at M,400, reaching an error of about 0.004 mH at M,900 sChan and Head-Gordon, 2002; Legeza et al., 2003ad.”
Quantum Chemistry in the Age of Quantum Computing. (2018, unknown): “imal-basis second-quantized Hamiltonian shown in Equation 101 to a four-qubit Hamiltonian Helec= 0I+ 1Z 1 + 2Z 2 + 3Z 3 + 4Z 1Z 2 (104) + 5Z 1Z 3 + 6Z 2Z 4 + 7X 1Z 2X 3 + 8Y 1Z 2Y 3 (105) + 9Z 1Z 2Z 3 + 10Z 1Z 3Z 4 + 11Z 2Z 3Z 4 (106) + 12X 1Z 2X 3Z 4 + 13Y 1Z 2Y 3Z 4 + 14Z 1Z 2Z 3Z 4”