Optimizing the density-matrix renormalization group method using quantum information entropy

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Abstract

In order to optimize the ordering of the lattice sites in the momentum space and quantum chemistry versions of the density-matrix renormalization group (DMRG) method we have studied the separability and entanglement of the target state for the one-dimensional Hubbard model and various molecules. By analyzing the behavior of von Neumann entropy we have found criteria that help to fasten convergence. An initialization procedure has been developed which maximizes the Kullback-Leibler entropy and extends the active space in a dynamical fashion. The dynamically extended active space procedure reduces significantly the effective system size during the first half-sweep and accelerates the speed of convergence of momentum space DMRG and quantum chemistry DMRG to a great extent. The effect of lattice site ordering on the number of block states to be kept during the RG procedure is also investigated.

Original languageEnglish
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume68
Issue number9
DOIs
Publication statusPublished - Nov 15 2003

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Quantum chemistry
renormalization group methods
Momentum
Entropy
quantum chemistry
entropy
Hubbard model
momentum
space density
Molecules
chemistry
molecules

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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title = "Optimizing the density-matrix renormalization group method using quantum information entropy",
abstract = "In order to optimize the ordering of the lattice sites in the momentum space and quantum chemistry versions of the density-matrix renormalization group (DMRG) method we have studied the separability and entanglement of the target state for the one-dimensional Hubbard model and various molecules. By analyzing the behavior of von Neumann entropy we have found criteria that help to fasten convergence. An initialization procedure has been developed which maximizes the Kullback-Leibler entropy and extends the active space in a dynamical fashion. The dynamically extended active space procedure reduces significantly the effective system size during the first half-sweep and accelerates the speed of convergence of momentum space DMRG and quantum chemistry DMRG to a great extent. The effect of lattice site ordering on the number of block states to be kept during the RG procedure is also investigated.",
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AB - In order to optimize the ordering of the lattice sites in the momentum space and quantum chemistry versions of the density-matrix renormalization group (DMRG) method we have studied the separability and entanglement of the target state for the one-dimensional Hubbard model and various molecules. By analyzing the behavior of von Neumann entropy we have found criteria that help to fasten convergence. An initialization procedure has been developed which maximizes the Kullback-Leibler entropy and extends the active space in a dynamical fashion. The dynamically extended active space procedure reduces significantly the effective system size during the first half-sweep and accelerates the speed of convergence of momentum space DMRG and quantum chemistry DMRG to a great extent. The effect of lattice site ordering on the number of block states to be kept during the RG procedure is also investigated.

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