Preprint 38-2014

Tensor product methods and entanglement optimization for ab initio quantum chemistry

Author(s) : Szilárd Szalay, Max Pfeffer , Gergely Barcza, Valentin Murg, Frank Verstraete, Reinhold Schneider , Örs Legeza

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 38-2014

MSC 2000

15A69 Multilinear algebra, tensor products

81-08 Computational methods

Abstract :
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, it is a common belief that 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 lectures given on the topic "New wavefunction methods and entanglement optimizations in quantum chemistry" at the Workshop on Theoretical Chemistry, 18 - 21 February 2014, Mariapfarr, Austria.

Keywords : tensor networks, DMRG, entanglement, tensor product approximation, quantum infromation