Tensor product methods and entanglement optimization for ab initio quantum chemistry

Szilárd Szalay, Max Pfeffer, Valentin Murg, Gergely Barcza, Frank Verstraete, Reinhold Schneider, Örs Legeza

Research output: Contribution to journalArticle

105 Citations (Scopus)


The treatment of high-dimensional problems such as the Schrödinger equation can be approached by concepts of tensor product approximation. We present general techniques that can be used for the treatment of high-dimensional optimization tasks and time-dependent equations, and connect them to concepts already used in many-body quantum physics. Based on achievements from the past decade, entanglement-based methods - developed from different perspectives for different purposes in distinct communities already matured to provide a variety of tools - can be combined to attack highly challenging problems in quantum chemistry. The aim of the present paper is to give a pedagogical introduction to the theoretical background of this novel field and demonstrate the underlying benefits through numerical applications on a text book example. Among the various optimization tasks, we will discuss only those which are connected to a controlled manipulation of the entanglement which is in fact the key ingredient of the methods considered in the paper. The selected topics will be covered according to a series of lectures given on the topic "New wavefunction methods and entanglement optimizations in quantum chemistry" at the Workshop on Theoretical Chemistry, February 18-21, 2014, Mariapfarr, Austria.

Original languageEnglish
Pages (from-to)1342-1391
Number of pages50
JournalInternational Journal of Quantum Chemistry
Issue number19
Publication statusPublished - Oct 1 2015


  • DMRG
  • entanglement
  • quantum infromation
  • tensor networks
  • tensor product approximation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

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